c.1200, "exempt, free from guilt" (e.g. 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- (cf. Old Saxon skiri, Old Frisian skire, German schier, Gothic skeirs "clean, pure"), from PIE root *(s)ker- (1) "to cut" (see shear (v.)).
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.
1620s, "deviate from course" (of a ship), of obscure origin, perhaps from Dutch scheren "to move aside, withdraw, depart," originally "to separate" (see shear (v.)). Related: Sheered; shearing. As a noun from 1660s.