infinitely (adv.)

late 14c., "eternal, limitless," also "extremely great in number," from Old French infinit "endless, boundless" and directly from Latin infinitus "unbounded, unlimited, countless, numberless," from in- "not, opposite of" (see in- (1)) + finitus "defining, definite," from finis "end" (see finish (v.)). The noun meaning "that which is infinite" is from 1580s.

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.