ballet (n.)

"dancing party, social assembly for dancing," 1630s, from French, from Old French baller "to dance," from Late Latin ballare "to dance," from Greek ballizein "to dance, jump about," literally "to throw one's body" (ancient Greek dancing being highly athletic), from PIE root *gwele- "to throw, reach." The extended meaning "very enjoyable time" is American English slang from 1945, perhaps 1930s in African-American vernacular.

"ballet enthusiast," by 1930, from ballet + -mane "one who has a mania for," which is ultimately from Greek and related to mania "madness."

*gwelə-, also *gwel-, Proto-Indo-European root meaning "to throw, reach," with extended sense "to pierce."

It forms all or part of: anabolic; arbalest; astrobleme; ball (n.2) "dancing party;" ballad; ballet; ballista; ballistic; ballistics; belemnite; catabolism; devil; diabolical; discobolus; emblem; embolism; hyperbola; hyperbole; kill (v.); metabolism; palaver; parable; parabola; parley; parliament; parlor; parol; parole; problem; quell; quail (v.) "lose heart, shrink, cower;" symbol.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit apa-gurya "swinging," balbaliti "whirls, twirls;" Greek ballein "to throw, to throw so as to hit," also in a looser sense, "to put, place, lay," bole "a throw, beam, ray," belemnon "dart, javelin," belone "needle," ballizein "to dance;" Armenian kelem "I torture;" Old Church Slavonic zali "pain;" Lithuanian galas "end," gėla "agony," gelti "to sting."