Counterintuitively, it may have originated from a world meaning lower-class—the Dutch heiden, "rustic, uncivilized man," which was related to heathen. The first usage in the OED is from 1668, describing what sounds like an orgy for widows: "The Widows I observ'd . . Chanting and Jigging to every Tune they heard, and all upon the Hoyty-Toyty like mad Wenches of Fifteen."
And the online etymological dictionary says:
also hoity toity, 1660s, "riotous behavior," from earlier highty tighty "frolicsome, flighty," perhaps an alteration and reduplication of dial. hoyting "acting the hoyden, romping" (1590s), see hoyden. Sense of "haughty" first recorded late 1800s, probably on similarity of sound.
Maybe it just goes to show that in the old days, the peasants had more fun. And when the landlords started having more fun—and looking down their noses at their renters/peasants—the word switched to them.
Snopes says that the popular etymology—haut toit, French for "high roof"—is false.