c. 1200, "exempt, free from guilt" (as in Sheer Thursday, the Thursday of Holy Week); later schiere "thin, sparse" (c. 1400), from Old English scir "bright, clear, gleaming; translucent; pure, unmixed," and influenced by Old Norse cognate scær "bright, clean, pure," both from Proto-Germanic *skeran (source also of Old Saxon skiri, Old Frisian skire, German schier, Gothic skeirs "clean, pure"), from PIE root *sker- (1) "to cut."
Sense of "absolute, utter" (sheer nonsense) developed 1580s, probably from the notion of "unmixed;" that of "very steep" (a sheer cliff) is first recorded 1800, probably from notion of "continued without halting." Meaning "diaphanous" is from 1560s. As an adverb from c. 1600.