1670s, of clothing, "adapted for being pinned up," from the verbal phrase (attested from mid-15c. in the sense "affix in a prominent place"), from pin (v.) + up (adv.). From 1940, in reference to pictures of "winsome young ladies in daring undress" ("Life," May 6, 1940) such as soldiers pinned up on their dugout walls, etc. The thing itself is older than the name. The noun in this sense is recorded from 1943.
"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.).