“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]