certainly (adv.)

c. 1300, "determined, fixed," from Old French certain "reliable, sure, assured" (12c.), from Vulgar Latin *certanus, extended form of Latin certus "determined, resolved, fixed, settled," of things whose qualities are invariable, "established," also "placed beyond doubt, sure, true, proved; unerring, to be depended upon" (also source of Old French cert, Italian certo, Spanish cierto), originally a variant past participle of cernere "to distinguish, decide," literally "to sift, separate." This Latin verb comes from the PIE root *krei- "to sieve," thus "discriminate, distinguish," which is also the source of Greek krisis "turning point, judgment, result of a trial" (compare crisis).

The transferred sense, in reference to persons, "full of confidence in one's knowledge or judgment, made certain in reference to a matter or thing," is from mid-14c. (it also was a sense in Latin). The meaning "established as true beyond doubt" in English is from c. 1400. The meaning "indefinite, not specifically named, known but not described" is from late 14c.

Different as this seems to be from sense I, it is hardly separable from it in a large number of examples: thus, in [a certain hour], the hour was quite 'certain' or 'fixed', but it is not communicated to the reader; to him it remains, so far as his knowledge is concerned, quite indefinite; it may have been, as far as he knows, at any hour; though, as a fact, it was at a particular hour. [OED]

Lewis & Short write that Latin certus also was sometimes indefinite, "of things, the certainty of whose existence is given, but whose nature is not more definitely designated, or comes not into consideration ...."

Hence the euphemistic use, attested from mid-18c., as in woman of a certain age "an old maid;" woman of a certain description "disreputable woman;" in a certain condition "pregnant;" a certain disease "venereal disease;" of a certain weight "obese." Used with proper names from 1785, "often conveying a slight shade of disdain" [OED]. Certainer, certainest were common to c. 1750, but have fallen from proper use for some reason. Expression for certain "assuredly" is attested by early 14c.

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.