to win something hands down (1855) is from horse racing, from a jockey's gesture of letting the reins go loose in an easy victory.
The Two Thousand Guinea Stakes was not the best contested one that it has been our fortune to assist at. ... [T]hey were won by Meteor, with Scott for his rider; who went by the post with his hands down, the easiest of all easy half-lengths. Wiseacre certainly did the best in his power to spoil his position, and Misdeal was at one time a little vexatious. [The Sportsman, report from April 26, 1840]
Ancient Greek had akoniti "without a struggle, easily," from akonitos (adj.), literally "without dust," specifically "without the dust of the arena."
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]