Is it farther or further?
type of dance, 1766, from French cotillion (15c.), originally "petticoat," a double diminutive of Old French cote "skirt" (see coat (n.)); its application to a kind of dance arose in France and is considered obscure by some linguists, but there are lively turns in the dance that flash the petticoats.
Meaning "formal ball" is 1898, American English, short for cotillion ball. French uses -on (from Latin -onem) to reinforce Latin nouns felt to need more emphatic power (e.g. poisson from Latin piscis). It also uses -on to form diminutives, often strengthened by the insertion of -ill-, as in the case of this word.
late 18th-century and 19th-century French court dance, popular also in England. A precursor of the quadrille, the cotillion was danced by four couples standing in a square set. The first and third, then the second and fourth, couples executed various series of geometric figures.