1540s, "a staff used as a weapon," from Fr. batôn "stick, walking stick, staff, club, wand," from O.Fr. baston (12c.) "stick, staff, rod," from L.L. bastum "stout staff," probably of Gaulish origin or else from Gk. *baston "support," from bastazein "to lift up, raise, carry." Meaning "staff carried as a symbol of office" is from 1580s; musical sense of "conductor's wand" is from 1867.
"strip of wood (especially used to fasten canvas over ships' hatches)," 1650s, Anglicized variant of baton "a stick, a staff" (see baton). Nautical use attested from 1769. As a verb, "to furnish with battens," attested from 1775; phrase batten down recorded from 1823.
1876, in ref. to downward stroke of a conductor's baton; 1952 in fig. sense of "pessimistic," but probably just from the association of the word down, since the beat itself is no more pessimistic than the upbeat (q.v.) is optimistic.
"with a positive mood," 1947, apparently from the musical noun upbeat (1869), referring to the beat of a bar at which the conductor's baton is in a raised position; the "optimistic" sense apparently for no other reason than that it sounds like a happy word (the musical upbeat is no more inherently "positive" than any other beat).
"officer's servant," originally military title for "man in charge of a bat-horse and its load," 1755, from bat "pack-saddle" (late 14c.), from O.Fr. bast (Mod.Fr. bât), from L.L. bastum (see baton). Hence also batwoman (1941).
O.E. stæf "walking stick, strong pole used for carrying, rod used as a weapon" (also, in plural, "letter, character, writing," cf. stæfcræft "grammar"), from P.Gmc. *stabaz (cf. O.S. staf, O.N. stafr, O.Fris. stef, M.L.G., M.Du. staf, O.H.G. stab, Ger. Stab, Goth. *stafs "element;" M.Du. stapel "pillar, foundation"), from PIE base *stebh- "post, stem, to support, place firmly on, fasten" (cf. O.Lith. stabas "idol," Lith. stebas "staff, pillar;" O.C.S. stoboru "pillar;" Skt. stabhnati "supports;" Gk. stephein "to tie around, encircle, wreathe," staphyle "grapevine, bunch of grapes;" O.E. stapol "post, pillar"). Sense of "group of military officers that assists a commander" is attested from 1702, apparently from Ger., from the notion of the "baton" that is a badge of office or authority (a sense attested in Eng. from 1535). Meaning "group of employees (as at an office or hospital)" is first found 1837. The verb meaning "to provide with a staff of assistants" is from 1859. Staff of life "bread" is from the Biblical phrase "to break the staff of bread" (Lev. xxvi.26), transl. Heb. matteh lekhem.