Origin and history of keenly

c. 1200, kene, from Old English cene "bold, brave, fearless," in later Old English "clever, prudent, wise, intelligent," common Germanic (cognate with Old Norse kænn "skillful, wise," Middle Dutch coene "bold," Dutch koen, Old High German kuon "pugnacious, strong," German kühn "bold, daring"), but according to OED there are no cognates outside Germanic and the original meaning is "somewhat obscure"; it seem to have been both "brave" and "skilled." Perhaps the connection notion was "to be able" and the word is connected to the source of can (v.1).

Sense of "eager (to do something), vehement, ardent" is from c. 1300. The physical meaning "sharp, sharp-pointed, sharp-edged" (c. 1200) is peculiar to English. Extended senses from c. 1300: Of sounds, "loud, shrill;" of cold, fire, wind, etc. "biting, bitter, cutting." Of eyesight c. 1720. A popular word of approval in teenager and student slang from c. 1900. Keener was 19c. U.S. Western slang for a person considered sharp or shrewd in bargaining.

common adverbial suffix, forming, from adjectives, adverbs signifying "in a manner denoted by" the adjective; Middle English -li, from Old English -lice, from Proto-Germanic *-liko- (source also of Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko). See -ly (1). It is 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.