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.
The motto is often translated as "He (God) is favorable to our undertakings," but this is not the only possible translation. Thomson wrote: "The pyramid signifies Strength and Duration: The Eye over it & Motto allude to the many signal interpositions of providence in favour of the American cause." The original design (by William Barton) showed the pyramid and the motto Deo Favente Perennis "God favoring through the years."
The Latin elements are the perfective of annuere "indicate approval, agree to, grant," literally "nod to (as a sign)" (from assimilated form of ad "to;" see ad-, + nuere "to nod;" see numinous) + perfect passive of coeptus, past participle of coepere "to begin, commence."