c. 1300, "unscathed, unhurt, uninjured; free from danger or molestation, in safety, secure; saved spiritually, redeemed, not damned;" from Old French sauf "protected, watched-over; assured of salvation," from Latin salvus "uninjured, in good health, safe," related to salus "good health," saluber "healthful," all from PIE *solwos from root *sol- "whole, well-kept."
As a quasi-preposition from c. 1300, on model of French and Latin cognates. From late 14c. as "rescued, delivered; protected; left alive, unkilled." Meaning "not exposed to danger" (of places) is attested from late 14c.; of actions, etc., "free from risk," first recorded 1580s. Meaning "sure, reliable, not a danger" is from c. 1600. Sense of "conservative, cautious" is from 1823. Paired alliteratively with sound (adj.) from late 14c. The noun safe-conduct (late 13c.) is from Old French sauf-conduit (13c.).
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.