1670s, "from moment to moment, every moment," from moment + -ly (2). Meaning "at any moment" is attested from 1775.
Entries linking to momently
moment n.
late 14c., "very brief portion of time, instant," in moment of time, from Old French moment (12c.) "moment, minute; importance, weight, value" and directly from Latin momentum "movement, motion; moving power; alteration, change;" also "short time, instant" (also source of Spanish, Italian momento), contraction of *movimentum, from movere "to move" (from PIE root *meue- "to push away").
Some (but not OED) explain the sense evolution of the Latin word by notion of a particle so small it would just "move" the pointer of a scale, which led to the transferred sense of "minute time division."
In careful use, a moment has duration, an instant does not. The sense of "notable importance, 'weight,' value, consequence" is attested in English from 1520s. Meaning "opportunity" (as in seize the moment) is from 1781.
In for the moment "temporarily, so far as the near future is concerned" (1883) it means "the present time." Phrase never a dull moment is attested by 1885 (Jerome K. Jerome, "On the Stage - and Off"). Phrase moment of truth first recorded 1932 in Hemingway's "Death in the Afternoon," from Spanish el momento de la verdad, the final sword-thrust in a bull-fight.
-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.