"mature," late 14c., past-participle adjective from grow up. The noun meaning "adult person" is from 1813, short for grown-up person, etc.
"a working to overtake a leading rival," by 1971, probably a figurative use from U.S. football in reference to being behind in the score. The verbal phrase catch up was used from early 14c. in the sense of "raise aloft," it is attested from c. 1400 as "to take up suddenly," and by 1846 in the sense of "get to the same point, overtake;" see catch (v.) + up (adv.).
also makeup, "manner in which something is put together," 1821, from the verbal phrase (see make (v.) + up (adv.)). To make up "build, collect into one form by bringing together" is from late 14c., also "prepare." It is attested from late 15c. as "supply as an equivalent," from 1660s as "end a quarrel, reconcile, settle differences, become friends again," by 1825 as "to fabricate artfully" (a story, etc.).
In reference to an actor, "prepare for impersonating a role" (including dress and the painting of the face), by 1808. Hence the noun sense of "appearance of the face and dress" (1858) and the sense of "cosmetics," attested by 1886, originally of actors.