Early instances of the form
One of the earliest examples of the form "this here NOUN" that a (concededly) scattershot series of Google Books searches finds is from James Fennimore Cooper, The Pioneers, or, The Sources of the Susquehana (1823):
"But d'ye see see, Squire, I kept my hatches close, and it is but little water that ever gets into my scuttle-butt. Harkee, Master Kirby! I've followed the salt water for the better part of a man's life, and have seen some navigation of the fresh; but this here matter I will ay in your favour, and that is, that you're awk'ardest green'un that ever straddled a boat's thwart.
An earlier (albeit satirical) example comes from England. From Chesterfield Burlesqued; or School for Modern Manners, third edition (1811):
In relating a story be sure to embellish it with, So said I, and said he to me, and I said to him again, and so said she, you take me right, you are up I see to what I mean, that there fellow understands a thing or two, but this here matter is neither here nor there, the worserer the betterer, in some of they cases, in that there sort of manner, &c.
And earlier still, from Tobias Smollett, The Adventures of Sir Launcelot Greaves (1760):
"Now this here elixir, sold for no more than sixpence a vial, contains the essence of the alkahest; the archæus, the catholicon, the menstruum, the sun, the moon; and, to sum up all in one word, is the true, genuine, unadulterated, unchangeable, immaculate, and specific chruseon pepuromenon ek puros."
An early dictionary notice of "this here" and "that there" occurs in Bartlett, Dictionary of Americanisms (1848):
THIS HERE and THAT THERE. These vulgar pleonasms are often heard in this country as well as in England.
Bartlett provides two examples of "this here" in the course of illustrating other Americanisms:
Some feller jest come and tuck my bundle and the jug of spirits, and left me in this here fix. —[William Tappan Thompson], [Major Jones's] Chronicle of Pineville (1845), p. 47
"Brethurn and sisturn, it's a powerful great work, this here preaching of the gospel, as the great apostle hisself allows in them words of hissin what's jest come into my mind ; for I never knowed what to preach till I ris up." —[Robert] Carlton [pseudonym of Baynard Rush Hall], The New Purchase[; or Seven and a Half Years in the Far West] (1843), vol. 1, p. 203
The first book is set in the fictitious town of Pineville, Georgia; the second describes life in the 1820s in Indiana (at the time, the Far West). In both instances the authors seem to be playing up the uncouthness of the quoted person.
Another phrase from the same family is the plural phrase "them there NOUN," which we see in action in this passage from Clerus, "Bright Sunbeams in Dark Dwellings: A Tale of the Coventry Distress," (1861), a British novel:
The window was again drawn up, and "coachy" was left to his own soliloquy once more. "Well now, that's what I call a pretty face if ever there was one, and them there eyes of hers are reg'lar beauties. I should think they've got what these bookmakers call 'hexpression.' And she 's so kind-like to the two old uns ; that looks good of her, and makes her prettier than ever in my 'pinion. ..."
The American jazz/blues song "Them There Eyes," by the way, was published in 1930, according to Wikipedia.
Scholarly identification and condemnation of the form
Perhaps the earliest scholarly (or scholastic) condemnation of "this here" and "those there" occurs in Anonymous, Errors of Pronunciation and Improper Expressions Used Frequently and Chiefly by the Inhabitants of London (1817):
THIS HERE, THAT THERE, for This, That. These expressions are very low.
The next to chime in is George Jackson, Popular Errors in English Grammar, Particularly in Pronunciation, Familiarly Pointed Out (1830), whose treatment of the subject seems remarkably similar to that of his predecessor:
This, not this here. That, (pro[nounced] that, not thet) not that there. [This here and that there are] very low.
All that there sort of thing, (low.)
Jackson reserves the characterizations "low" and "very low" for what he views as the worst affronts to English as spoken by the well-bred—blunders such as axed and ass'd (for "asked"), as how (under any circumstances), blow me if I do ("exceedingly low"), botheration seize it ("very vulgar"), chuck it to me (use "throw it to me"), drownded, 'tis all gammon, grub (for "meal"), his'n and her'n and our'n and their'n and your'n, howsomdever (for "however"), unproper, no more of your jaw (very low and blackguard-like"), a lark and sky-larking, obstropolous (for "obstreperous"—"exceedingly low"), hoile or ile (for "oil"), rum (in the sense of laughable), row (for "quarrel"), summat (for "somewhat"), etc. To sum things up, "All SLANG language is vilely low." A feller could git hisself a perdigious edycation from all them idears.
On the U.S. side of the Atlantic, Richard Bache, Vulgarisms and Other Errors of Speech (1869) lays down the law with regard to "this here" and "that there," in his chapter on "Tautological Phrases":
The use of this here, and of that there, instead of this and that, is incorrect. Alone, the word this, or the word that, relates to one of two things, this referring to the one near, that to the one more remote. In like manner, referring to two sets of things, these relates to the one near, and those to the one more remote.
Echoing (indeed, rather more than echoing, given that he doesn't acknowledge Bache's prior use of the same wording) is William Swinton, Language Lessons: An Introductory Grammar and Composition for Intermediate and Grammar Grades (1877):
The use of this here, and of that there, instead of this and that, is incorrect. The word this expresses all that can be denoted by "this here," and that expresses all that can be denoted by "that there." (This way of speaking is a sure sign of a want of education in the person using it.)
Frank Vizetetelly, A Desk-book of Errors in English (1906) was simply restating the established rule in his discussion of "that there":
that there : An illiterate expression commonly used with the mistaken idea that the use of "there" adds emphasis to what follows, as, "That there man." Say, rather, "That man there" or simply, and preferably "That man."
Evidently, the world of nineteenth-century and early twentieth-century grammar rules was very much like the world of Internet-based information today: One person says something, and then other people copy it and call it their own. Thus are rules (then) and facts (now) created.
Moreover, in the commentators' deep-seated horror of "low" or "illiterate" speech, we see the truth of John Lawler's remark (above) that the reason these forms are nonstandard "is that the wrong people talk that way."
How the form may have evolved
One way to think of the expression "this here NOUN [is X]" is as an expression evolved from "this here [is X]" in order to make the connection between this and the intended noun referent more emphatic or obvious. Instances of "this here" without an immediately following noun go back centuries. One early example that a Google Books search turns up is from a 1602 translation of Innocent Gentillet, A Discourse Upon the Meanes of Wel Governing (1602):
Dr Camines to prove his alleged saying, setteth down other examples, The Partialitie of the houses of Lancaster and Yorke in England, whereby the house of Lancaster was altogether ruined and brought downe, and the one house delivered to the other, seven or eight battailes betwixt three and fourscore princes of the royall blood of England and an infinit number pf people. This here is no small thing, but it is rather an example, which should make us abhorre all Partialities.
Likewise, from a translation of The Morals of Confucius, a Chinese Philosopher, second edition (1706):
The great Secret, says Confucius, to acquire true Knowledge, the Knowledge, consequently, worthy of Princes, and the most Illustrious Personages, is to cultivate and polish the Reason, which is a Present that we have received from Heaven. Our Concupiscence has disordered it, and intermixt several Impurities therewith. Take away therefore, and remove from it these Impurities, to the end that it may reassume its former Lustre, and enjoy its utmost Perfection. This, here is the Sovereign Good. This is not sufficient. 'Tis moreover requisite, that a Prince by his Exhortations, and by his own Example, make of his People, as it were, a new People.
And from Matthew Henry, An Exposition of All the Books of the old and New Testament (1708–1710):
It will be a surprising day, as the deluge was to the old world, ver. 37, 38, 39. That which he here intends to describe, is, the posture of the world at the coming of the Son of man ;besides his first coming to save, he has other comings, to judge: He saith, (John, x. 39.) For judgment I am come : and for judgment he will come ; for all judgment is committed to him, both that of the word, and that of the sword.
Now this here is applicable,
(4.) To temporal judgments, particularly that which was now hastening upon the nation and people of the Jews : Though they had fair warning give them of it, and there were many prodigies that were presages of it, yet it found them secure, crying, Peace and safety, 1 Thess. v. 3.
In each case it would not be a huge step to bring the referent noun into closer proximity to this, either in the form "this NOUN here" or the form "this here NOUN," yielding from Gentillet's sentence, "This example here" or "This here example"; from Confucius's, "This result here" or "This here result"; and from Henry's, "this biblical passage here" or "this here biblical passage."
In fact, the same Cooper novel cited above includes an instance of "this here" without a following noun, as well as the instance of "this here matter" already noted (both are spoken by the same character, a "steward" named Benjamin Pump):
"Why, yes, it was about their minds, I believe, Squire," returned the steward; "and by what I can learn, they spoke them pretty plainly to one another. Indeed, I may say that I overheard a small matter of it myself, seeing that the windows was open, and I hard by. But this here is no pick, but an anchor on another man's shoulder; and here's the other fluke down his back, maybe a little too close, which signifies that the lad has got under way and left his moorings."
So if we can trust Cooper's ear for colloquial speech, which Mark Twain says emphatically that we cannot, we may take The Pioneers as identifying a common colloquial speech pattern in which the referent noun in a "this here NOUN" phrase is sometimes made explicit and sometimes not.
Status of the "this here NOUN'/'that there NOUN' form today
As other commenters have said, the form "this here NOUN"/"that there NOUN" continue carry a lower-class/underclass/hicks-from-the-sticks stigma in the view of many educated people. The notion that it is primarily a southern/backwoods expression is not entirely sustained by usage. For example, I recall that on the Patti Smith album Horses, the narrator of her version of the Them/Van Morrison song "Gloria" says, in a New Jersey accent,
I go to this here party, and I—I just get bored
a narrative that suddenly changes tempo when the narrator first sets eyes on G-L-O-R-I-A. Smith was born in Chicago, lived for a while in Philadelphia, and then moved to Deptford, New Jersey—right across the Delaware River from Philadelphia. Neither Smith nor her family were from the South or from rural backgrounds. For Smith, I suspect, a character who says "I go to this here party" isn't a rustic but a tough guy—lower-middle-class, indifferent about education, cocky. But others' interpretations, no doubt, will vary.