"greatly, much," 1620s, from much + -ly (2). Now obsolete or slang. Middle English simply used much as an adverb.
Entries linking to muchly
much adj.
c. 1200, "great in quantity or extent" (also "great in size, big, large," a sense now obsolete), a worn-down form (by loss of unaccented last syllable) of Middle English muchel "large, tall; many, in a large amount; great, formidable," from Old English micel "great in amount or extent," from Proto-Germanic *mekilaz, from PIE root *meg- "great."
As a noun, "a large quantity, a great deal," and as an adverb, "in a great degree, intensely, extensively," from c. 1200. Since 17c. the adverb has been much-used as a prefix to participial forms to make compound adjectives. For vowel evolution, see bury. Too much was used from late 14c. in the senses "astonishing, incredible," also "too offensive, unforgivable." Much-what "various things, this and that" (late 14c.) was "Very common in the 17th c." [OED] and turns up in an 1899 book of Virginia folk-speech as well as "Ulysses."
-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.