1540s, "conveniently," from handsome + -ly (2). Meaning "attractively" is from 1610s; "liberally, generously" from 1735.
Entries linking to handsomely
handsome adj.
c. 1400, handsom "easy to handle, ready at hand," from hand (n.) + -some (1). Sense extended to "fit, appropriate" (1550s, implied in handsomely), then "having fine form, good-looking, agreeable to the eye" (1580s). Meaning "generous, on a liberal scale" (of rewards, etc.) first recorded 1680s.
[Americans] use the word "handsome" much more extensively than we do: saying that Webster made a handsome speech in the Senate: that a lady talks handsomely, (eloquently:) that a book sells handsomely. A gentleman asked me on the Catskill Mountain, whether I thought the sun handsomer there than at New York. [Harriet Martineau, "Society in America," 1837]
Bartlett (1848) quotes Webster (the lexicographer) on this colloquial American use of handsome: "In general, when applied to things, it imports that the form is agreeable to the eye, or to the taste; and when applied to manner, it conveys the idea of suitableness or propriety with grace." Related: Handsomeness. For sense development, compare pretty (adj.), fair (adj.). Similar formation in Dutch handzaam "tractable, serviceable."
Handsome is founded upon the notion of proportion, symmetry, as the result of cultivation or work; a handsome figure is strictly one that has been developed by attention to physical laws into the right proportions. It is less spiritual than beautiful; a handsome face is not necessarily a beautiful face. [Century Dictionary, 1895]
-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.