Middle English sharpli, from Old English scearplice "acutely, keenly; painfully, severely; attentively, quickly;" see sharp (adj.) + -ly (2). Old English also had adverbial form scearpe "sharply."
Entries linking to sharply
sharp adj.
Old English scearp "having a cutting edge; pointed; intellectually acute, active, shrewd; keen (of senses); severe; biting, bitter (of tastes)," from Proto-Germanic *skarpaz, literally "cutting" (source also of Old Saxon scarp, Old Norse skarpr, Old Frisian skerp, Dutch scherp, German scharf "sharp"), from PIE root *sker- (1) "to cut" (source also of Lettish skarbs "sharp," Middle Irish cerb "cutting").
The figurative meaning "acute or penetrating in intellect or perception" was in Old English; hence "keenly alive to one's own interests, quick to take advantage" (1690s). Of words or talk, "cutting, sarcastic," from early 13c. Meaning "distinct in contour" is from 1670s. The musical meaning "half step above (a given tone)" is from 1570s. Meaning "stylish" is from 1944, hepster slang, from earlier general slang sense of "excellent" (1940). Phrase sharp as a tack first recorded 1912 (sharp as a needle has been around since Old English). Sharp-shinned attested from 1704 of persons, 1813 of hawks.
-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.