As the poster notes, Merriam-Webster Online provides two definitions for entitled as an adjective:
entitled adjective 1 : having a right to certain benefits or privileges [Example:] After having saved the country, ain't they entitled to help themselves to just as much of it as they want? — Mark Twain 2 : having or showing a feeling of entitlement (see entitlement sense 2 ["belief that one is deserving of or entitled to certain privileges"]) [Example:] spoiled, entitled children | his entitled attitude/behavior | leading an entitled life | We are also the so-called entitled generation, … told by helicopter parents and the media, from the moment we exited the womb, that we could be "whatever we wanted" … — Jessica Bennett
First Known Use of entitled: 1817, in the meaning defined at sense 1
Nevertheless, entitled as an adjective has never appeared in an edition of Merriam-Webster's Collegiate Dictionary series—the most recent edition being the eleventh edition (2003), suggesting that widespread use of the adjective as anything more than an occasional extension of one of the two senses of the verb entitle that Merriam-Webster Online identifies—
entitle transitive verb 1 : to give a title to : DESIGNATE 2 : to furnish with proper grounds for seeking or claiming something [Example:] this ticket entitles the bearer to free admission"
—is a fairly recent phenomenon. I note that those two definitions of entitle have also appeared in the past four print editions of the Collegiate Dictionary, starting with the eighth edition (1973). The seventh edition (1963) had a somewhat different formulation, although the net effect of the wording seems not much different:
entitle vt 1 : to give a title to : DESIGNATE 2 a : to give a legal right to b : to qualify for something
Evidently, the lexicographers at Merriam-Webster decided at some point between 1963 and 1973 that the "legal right" sense of entitle was just a special case of the broader "qualify for" (or "furnish with proper grounds for" meaning, rather than being a fundamentally distinct meaning.
Early examples of 'entitled' as an adjective in the form 'an entitled X'
Database searches for instances of entitled as an adjective in phrases of the form "an entitled X," where X refers to a person or group of people, yield matches going back to the 1940s. In those early instances, however, the meaning of entitled is "having a proper claim [to some status of thing]." For example, from "After the War: Federal Government's Plans for Servicemen," in the [Perth, Western Australia] West Australian (March 24, 1945):
Unless he could show reasonable and substantial cause for not doing so an employer was bound to engage a person entitled to preference. In deciding whether reasonable cause existed for not engaging an entitled person, the employer was required to consider the length, locality and nature of the service of the persons entitled, and their qualifications as compared with other applicants.
From "Digger Digest," in the Cairns [Queensland] Post (October 26, 1948):
Campaign stars for the second World War have been disgracefully turned out. No numbers or names are to be stamped or engraved on the back, and consequently they become worthless. The R.S.L. intends to purchase a stamping machine, and will stamp on the star of an entitled member his name and regimental number, but this is not the answer to the problem. The Government should follow the precedent established in the first World War, or not issue campaign medals at all.
From "Social Security Increases," in the Oxford [Michigan] Leader (July, 24, 1957):
At the end of 1956. monthly benefit payments were going to 3,655 wives or aged dependent husbands of old-age beneficiaries and to 2,838 aged widows or dependent aged widowers and parents in Oakland County.
The 12-month increase in aged beneficiaries is due partly to the lowering from 65 to 62 of the age at which a woman without an entitled child in her care may qualify for benefits, Mr. LaRock said.
From His Majesty's Government Gazette (Federation of Malaya) [snippet view]:
"pensionable emoluments" means the pensionable emoluments as defined in Regulation 2 of the Pension Regulations being received by an entitled officer at the date on which his service terminates; ...
From "$27,000 Monthly Paid in Survivor Benefits to 750 Neck Residents," in the [Warsaw, Virginia] Northern Neck News (November 20, 1958):
Child benefits are payable to the worker's natural, adopted, or step-children who are unmarried, under age 18, and either living with or receiving support from the worker at the time of his death. Benefits are also payable to children over age 18 who are disabled since before reaching that age.
Benefits are payable to widows who have not remarried and have reached age 62 or have an entitled child in their care.
From U.S. Congress, House Committee on Ways and Means, Disability Insurance Fact Book: A Summary of the Legislative and Administrative Development of the Disability Provisions in Title II of the Social Security Act (1959):
DISABILITY INSURANCE BENEFITS: CONDITIONS OF ENTITLEMENT
The Social Security Act provides for the payment of a monthly disability insurance benefit to an entitled individual. An individual is entitled if he is insured; has attained the age of 50, but has not as yet attained the age of 65; is under a disability; files an application.
And from U.S. Department of Health, Education, and Welfare, "Analysis of Benefits OASDI Program 1960 Amendments" (1960):
Types of Benefits. ... The third type, so-called death benefits, is available upon his death to the survivors of an insured worker as well as to the surviving dependents of an entitled primary beneficiary.
This same study refers to also alludes to "an entitled primary beneficiary" a second time, as well as to "an entitled child" (four times), "an entitled child beneficiary" (four times), and "an entitled survivor" (once).
Early examples of 'entitled' in the newer sense, in the form 'an entitled X'
The earliest instance of "an entitled" in the sense of "arrogant, spoiled, or possessed of an unjustified sense of deserving deference or special favorable treatment" is from Arlene Peck, "Women Go Through Life with Gusto," in the [Indianapolis, Indiana] Jewish Post (June 17, 1987):
And, for whatever reason, people expect too much. According to William Novak, who wrote The Great American Man Shortage, "We live in an entitled society. People are now walking out of marriages that are about 70 percent satisfying. In the past, that would have been enough reason to stay married. But today, people think thy are entitled to 100 percent. So the first thing they do after they get divorced is to go out and try to find somebody who embodies that missing 30 percent."
From Jeralyn Jones, "The Psychiatrist's Perspective," in Robert Surber, Clinical Case Management: A Guide to Comprehensive Treatment of Serious Mental Illness (1994):
Sam was a client who had been followed by case management for 5 years. He was known as an entitled man who never thanked or attempted to please his caregivers. Interpretations would send him out the door, swearing never to return to the clinic. This behavior was understood as Sam's method of distancing from ...
And from Jon Mills & Janusz Polanowski, Ontology of Prejudice (1997):
A cardinal dilemma facing White society is that Whites are being confronted with whether they want to give up their privilege, namely, their special status of advantage and power. Whites are used to being "number one." They are not accustomed to giving up what was in the past never questioned. The White in bad faith sees this advantage as a "right," an entitled position superior in status that should not be questioned.
This last instance is notable for applying the "arbitrarily claiming to the right to enjoy or exercise special privileges" sense of entitled to a viewpoint rather than to a person or group of people—but the connection in this case of the "entitled position" to the people making the claim on their own behalf is clear enough.
When did 'entitled' in its new sense of 'spoiled' or 'illegitimately claimed' arise?
The Language Log discussion of the relatively late-to-emerge meaning of entitlement as "an illegitimate claim," mentioned in user121863's comment above, argues that the origin of this usage was in psychoanalytical jargon:
In the 1960s, psychoanalysts also start using entitled and entitlement with strongly negative connotations, resulting in the emergent term of art "narcissistic entitlement".
Unfortunately, the four examples of such usage from the period 1964–1972 that the Language Log post mentions involve the noun entitlement or the noun phrase narcissistic entitlement. It would certainly make sense for the adjective entitled in a relatedly negative sense to have emerged from the same psychoanalytic usage—and the example I cite above from 1994 seems to demonstrate such a connection—but the post doesn't present any examples of entitled in the form "an entitled X." The closest it comes to offering one is in this quotation from Soma Golden, "Ash Hints at Need to Cut Social-Program Benefits," in the New York Times (August 24, 1974):
Until now, the Government’s so-called "entitlement" programs — which include Social Security, Medicare and Medicaid, veterans’ benefits, welfare and retirement — have been considered virtually untouchable by Federal budget-cutters. Benefit levels and eligibility requirements are specified in legislation and few politicians have wanted to risk disappointing voters who feel "entitled" to their share.
But this really isn't an example of entitled being used to mean "illegitimately claiming to deserve or be entitled to certain privileges"; to the contrary, it's an example of entitled being used to mean "having a legitimate claiming to certain privileges." At any rate, that's what the writer indicates the voters in this sentence feel. The feeling my be illegitimate, but the word "entitled"—even packaged in quotation marks—doesn't mean "spoiled" or "illegitimate."
In a comment above, Colin Fine reports that the OED cites Robert Coles, Privileged Ones: The Well-off and the Rich in America (1977) as using entitled in the relevant sense. The word appears on at least nine pages of Coles's book, but according to a Wikipedia Language Desk discussion from January 16, 2017, the following text block is the one that the OED's example comes from:
Such counsel is not as callous as it may sound—or, ironically, as it may well have been intended to sound. The child who hears it gets briefly upset, but "a fast pickup" does indeed take place quite often. Again, it is a matter of feeling "entitled." A child who has been told repeatedly that all he or she needs to do is try hard does not feel inclined to allow himself or herself much skeptical self-examination. The point is to feel entitled—then act upon that feeling. The boy whose composition was just quoted from used the word "entitled" in another essay he wrote, this one meant to be a description of his younger (age five) brother. The writing was not, however, without an autobiographical strain to it: "I was watching my brother from my bedroom window. He was climbing up the fence we built for our corral. He got to the top, and then he just stood there and waved and shouted. No one was there. He was talking to himself. He was very happy. Then he would fall. He would be upset for a few seconds, but he would climb right back up again. Then he would be even happier! He was entitled to be happy. It is his fence, and he has learned to climb it, to stay up, and balance himself.
Coles's use of entitled is not much different from Golden's. In each case, the author uses the word to describe someone's sense of having the right or power to enjoy or achieve something—the element of illegitimacy either isn't there at all or is only obliquely hinted at. Indeed, Steven Weiland, Intellectual Craftsmen: Ways and Works in American Scholarship, 1935-1990 (1991) sees Coles as approving of the five-year-old child's confidence:
No one of course would argue with the assertion that privileged children generally have high expectations of what life has to offer. Coles, proposes, however, that a feeling of entitlement can and usually does develop without the parallel development of an excessively narcissistic tone. Children of wealthy families, he claims, have a realistic view of their lives as they exhibit predictable kinds of confidence. ... What is proprietary about this view [of the five-year-old boy as described by his brother in Coles's book] is seemingly less important to Coles than what is adaptive or "balanced" in the mind of the child.
The path to entitled in the sense of "arrogant, spoiled, or possessed of an unjustified sense of deserving deference or special favorable treatment" almost certainly began in psychology/psychoanalysis, where the appeared (no later than 1972) in connection with as a form of mental derangement or delusion, especially in connection with the term narcissistic entitlement, which itself arose no later than 1964. Subsequently, entitled migrated to sociology as a negative term associated with an unjustifiable claim or assumption of privilege coming at the expense of others.
Language Log asserts that entitled in a negative clinical psychological sense arose in the 1960s, and the OED cites what it considers a relevant example of entitled in a psychology/sociology text published in 1977. But the earliest instance I could find of entitled used in the relevant sense and in the form "an entitled [person or group of people]" is from 1987.