In addition to the historical threads that ScotM identifies in his excellent answer, several other -pies formations that were current in the 1960s and 1970s may have contributed to the adoption of yuppies as shorthand for members of the sociological category "young urban professionals." To wit: preppies, bippies, blippies, dippies, and trippies.
The term preppies goes back to at least 1963, when it appeared in the Harvard Alumni Bulletin, volume 66 [combined snippets]:
Despite University efforts to the contrary, House stereotypes continue to play a dominant role in the freshman's choice. Winthrop, he has heard, is for athletes; Eliot is filled with preppies and clubbies; Adams is literary or "beat"; Kirkland, "musical" and friendly; Quincy, political; Dunster, "gung-ho"; and so on: ...
A 1963 issue of The New Yorker reported that there was a "foolish, harmless musical spoof" called Preppies at The Promenade on Broadway at 76th Street that year.
Although most people of a certain age remember bippies as a euphemism for anatomical posteriors, popularized in 1967 by the cast of the TV show Rowan & Martin's Laugh-In, it was also a slang term,as explained in U.S. Senate Committee on the Judiciary, Methaqualone (Quaalude, Sopor) Traffic, Abuse and Regulation (1973):
San Francisco society chronicler Meria Zellerbach says she has heard of no run on dermatologists for silicone among that city's bippies (a term not so long ago in vogue for BPs, or Beautiful People, so designated by Women's Wear Daily), but of course plastic surgery to shore up sags and tighten against the stresses of age continues to be popular.
Another early reference to bippies suggests the jocular element in the usage. From Congressional Record (1969) [combined snippets]:
This wave of discontent, with all its ominous implications, doesn't come from the hippies, the bippies or the dippies. It doesn't come from the Far Left, the Far Right or the Far Anything.
It comes from citizens—your neighbors—— the men and women who have tried to fulfill their lives in honorable careers with the postal service.
And from Dairy and Ice Cream Field (1969) [combined snippets]:
Whether they're called Hippies, Bippies, Boy Scouts or Flower Children, teen-agers in the United States are spending money like mad.
The heyday of blippies is more of a blip. The term shows up in Reginald Major, A Panther Is a Black Cat (1971) [combined snippets]:
Reportedly the SNCC [Student Nonviolent Coordinating Committee] staff was wary of the Panthers. They did not accept the Panther ten-point program, and also rejected the idea of conducting black people's plebiscite. The plebiscite was a program thought up by Eldridge Cleaver, and SNCC might have rejected it on that basis. Cleaver had not exactly endeared himself to SNCC when he described them as being primarily composed of "blippies," black hippies.
The word dippies shows up in the duplicative term hippie-dippies and also as a (rather ill-defined) term on its own, essentially meaning "crazy people." From Henry Williamson, The Golden Virgin (1957) [combined snippets]:
You see, midear," he went on, in a different voice, as he pulled out the ends of his moustache with finger and thumb, "if you tell the jolly old doc. he may get me sent away among the genuine dippies, and I'm not really that, you know. You see what happens is this. I can't control my thoughts of what happened when that mine went up taking me for a joy ride. ..."
On the other hand, Merriam-Webster's Eleventh Collegiate Dictionary (2003) traces dippy as an adjective to 1899 (with "origin unknown") and says that it means "foolish." The word probably retained that sense as well as "a crazy person" when used as a noun later in the twentieth century.
The term trippies arose in connection with 1960s drug culture. From Liberation: An Independent Monthly (1966) [combined snippets]:
Hippie reject the System, and attempt to drop out from it in various ways, but many do not try to do so through drugs. It is important to distinguish between dropouts for whom drugs are the closest thing to an organizing life principle, and dropouts for whom sex or poetry or "community" or something else comes closest to an organizing life principle. I will here call the drug-centered people "trippies."
Hippies and trippies share a common point of departure—and I share it with them.
And from Tradition, volume 10 (1969) [combined snippets]:
Religious Experiences Not a few "trippies" have reported on the similarity of their experiences to the reports of religious mystics and quite a few papers have discussed the drug's religious implications.
Given the evident predilection in U.S. English for -pies forms, it is hardly surprising that Y.U.P.s should in short order become known as yuppies. They were followed in short order by buppies ("black urban professionals"), muppies ("Mennonite urban professionals), and (more recently) bappies ("booming aspirational and previously poor").