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."
early 14c. as a verbal phrase, "lift and take with the fingers," from pick (v.) + up (adv.). From 1510s as "take or get casually, obtain or procure as opportunity offers." Meaning "take (a person found or overtaken) into a vehicle or vessel," is from 1690s, also, of persons, "make acquaintance or take along" (especially for sexual purposes). Intransitive meaning "improve gradually, reacquire vigor or strength" is by 1741. Sense of "tidy up" is from 1861; that of "arrest" is from 1871; meaning "gain speed" is from 1922; meaning "to pay" (a check, tab, etc.) is from 1945. Pick-me-up "stimulating alcoholic drink" is attested from 1867.
[A]pplied to succession when divided so as to give the representatives belonging to one branch the share only that their head or ancestor would have taken had he survived. Thus, in a gift to A and the children of B, if they are to take per capita, each child will have a share equal to that of A; but if they are to take per stirpes, A will take one half and the other half will be divided among the children of B. [Century Dictionary]