Yours, Etc.: Origins and Uses of 8 Sign-Offs
"to droop, decline, tire," 1520s, apparently an alteration of flag (v.) in its sense of "droop." Transitive sense of "to make (someone or something) fatigued" is first attested 1826. Related: Fagged; fagging.
British slang for "cigarette" (originally, especially, the butt of a smoked cigarette), 1888, probably from fag-end "extreme end, loose piece" (1610s), from fag "loose piece" (late 15c.), which is perhaps related to fag (v.).
: frenetic hot-rhythm dancing, the cheap fag jokes/ like a fag partynoun
(also fagout) To fatigue; exhaust •The sense ''to study hard, go without sleep,'' is attested in Cambridge University slang by 1803: This sort of work fags me quickly (1930+)
[origin unknown; the ''homosexual'' sense may be connected with the British term fag, ''the boy servant, and inferentially the catamite, of a public-school upperclassman''; perhaps influenced by Yiddish faygele, ''homosexual,'' literally ''bird, little bird'']