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]
1520s, the earliest recorded sense is "mistress;" the allusion to grass is not clear, but it commonly was believed to refer to casual bedding (compare bastard and German Strohwitwe, literally "straw-widow," and compare the expression give (a woman) a grass gown "roll her playfully on the grass" (1580s), also euphemistic for the loss of virginity). Revived late 18c. as "one that pretends to have been married, but never was, yet has children;" in early 19c. use it could mean "married woman whose husband is absent" (and often presumed, but not certainly known to be, dead), also often applied to a divorced or discarded wife or an unmarried woman who has had a child. Both euphemistic and suggestive.
[G]rasse wydowes ... be yet as seuerall as a barbours chayre and neuer take but one at onys. [More, 1528]
GRASS WIDOW, s. a forsaken fair one, whose nuptials, not celebrated in a church, were consummated, in all pastoral simplicity, on the green turf. [Rev. Robert Forby, "Vocabulary of East Anglia," London, 1830]
"pursuit of anything in ignorance of the direction it will take," hence "a foolish enterprise," 1592, first attested in "Romeo and Juliet," where it evidently is a figurative use of an earlier (but unrecorded) literal sense in reference to a kind of follow-the-leader steeplechase, perhaps from one of the "crazy, silly" senses in goose (n.). Wild goose (as opposed to a domesticated one) is attested in late Old English (wilde gos).