late 14c., "commonly;" early 15c., "intimately;" from familiar + -ly (2).
Entries linking to familiarly
familiar adj.
mid-14c., "intimate, very friendly, on a family footing," from Old French famelier "related; friendly," from Latin familiaris "domestic, private, belonging to a family, of a household;" also "familiar, intimate, friendly," a dissimilation of *familialis, from familia (see family).
From late 14c. as "of or pertaining to one's family." Of things, "known from long association," from late 15c. Meaning "ordinary, usual" is from 1590s.
The noun meaning "demon, evil spirit that answers one's call" is from 1580s (familiar spirit is attested from 1560s); earlier as a noun it meant "a familiar friend" (late 14c.). The Latin plural, used as a noun, meant "the slaves," also "a friend, intimate acquaintance, companion."
-ly 2
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.