1520s, "plainly, obviously," from gross (adj.) + -ly (2). The meaning "coarsely, shamefully" is attested from 1540s; that of "excessively" is from 1610s.
Entries linking to grossly
gross adj.
mid-14c., "large;" early 15c., "thick," also "coarse, plain, simple," from Old French gros "big, thick, fat; tall; strong, powerful; pregnant; coarse, rude, awkward; ominous, important; arrogant" (11c.), from Late Latin grossus "thick, coarse" (of food or mind), in Medieval Latin "great, big" (source also of Spanish grueso, Italian grosso), a word of obscure origin, not in classical Latin. It is said to be unrelated to Latin crassus, which meant the same thing, or to German gross "large," but said by Klein to be cognate with Old Irish bres, Middle Irish bras "big."
Its meaning forked in English. Via the notion of "coarse in texture or quality" came the senses "not sensitive, dull stupid" (1520s), "vulgar, coarse in a moral sense" (1530s). Via the notion of "general, not in detail" came the sense of "entire, total, whole, without deductions" (early 15c.), as in gross national product (1947). The meaning "glaring, flagrant, monstrous" is from 1580s; modern meaning "disgusting" is first recorded 1958 in U.S. student slang, from earlier use as an intensifier of unpleasant things (gross stupidity, etc.).
-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.