1707, "paper duly authenticated by a signature and otherwise blank, left to someone to be filled in at his discretion," French, literally "white paper," from carte (see card (n.1)) + blanche, from Old French blanc "white," a word of Germanic origin (see blank (adj.)). The figurative sense of "full discretionary power, unrestricted permission or authority in some manner" is from 1766. Compare the native blank check, used in the same figurative sense.
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.