"precisian in speech or manners," 1753, originally in reference to theological scruples (1704), of unknown origin; earlier appearances of the same word meaning "dandy, fop" (1670s), "thief" (c.1600; in form prigger recorded from 1560s) could be related, as could thieves' cant prig "a tinker" (1560s).
A p[rig] is wise beyond his years in all the things that do not matter. A p. cracks nuts with a steam hammer: that is, calls in the first principles of morality to decide whether he may, or must, do something of as little importance as drinking a glass of beer. On the whole, one may, perhaps, say that all his different characteristics come from the combination, in varying proportions, of three things--the desire to do his duty, the belief that he knows better than other people, & blindness to the difference in value between different things. ["anonymous essay," quoted in Fowler, 1926]Related: Priggery.