"temporary marked increase in the birth rate," coined 1941 from baby (n.) + boom (n.2); derivative baby-boomer (member of the one that began in the U.S. in 1945) is recorded by 1963 (in newspaper articles when they began to approach college age); earlier it had sometimes meant "a young kangaroo."

in figurative sense of "withdraw a charge," 1859, American English, from the notion of descending a ladder, etc. (such a literal sense is attested by 1849); from back (v.) + down (adv.).

"retreat, stop annoying someone," by 1938, from the verbal phrase, from back (v.) + off (adv.).

also back-seat, 1832, originally of coaches, from back (adj.) + seat (n.). Used figuratively for "less or least prominent position" by 1868. Back-seat driver "passenger who gives the driver unwanted advice" is attested by 1923.

You know him. The one who sits on the back seat and tells the driver what to do. He issues a lot of instructions, gives advice, offers no end of criticism and doesn't do a bit of work. ["The Back Seat Driver," Wisconsin Congregational Church Life, May 1923]

1767, "stand behind and support," from back (v.) + up (adv.). The meaning "move or force backward" is by 1834. Of water prevented from flowing, by 1837.

a type of prisoner's restraint, 1818; used figuratively by 1883 of foolish, wasteful habits; as "one's wife," 1920.

"small Central American state with an economy dependent on banana production," 1901, American English.

also barb wire, "fencing wire with sharp edges or points," 1863, American English; see barb (n.) + wire (n.). Originally for the restraint of animals.

1919, American English, originally a reference to rumors of quadriplegics as a result of catastrophic wounds suffered in World War I (the U.S. military authorities vehemently denied there were any such in its hospitals), from basket (n.) + case (n.2). Probably literal, i.e., stuck in a basket, but basket had colloquial connotations of poverty (begging) and helplessness long before this. The figurative sense of "person emotionally unable to cope" is from 1921.

see bate (v.1).