1540s, "long loose gown or outer cloak," from French casaque "long coat" (16c.), corresponding to Spanish casaca, Italian casacca, probably ultimately from Turkish quzzak "nomad, adventurer," (the source of Cossack), from their typical riding coat. Or perhaps from Arabic kazagand, from Persian kazhagand "padded coat," from kazh "raw silk" + agand "stuffed." Chiefly a soldier's cloak 16c.-17c.; ecclesiastical use is from 1660s.
"belt, girdle, or band worn round the body," 1580s, from Latin cinctura "a girdle," from cinctus, past participle of cingere "to surround, encircle" (see cinch (n.)). Especially the girdle used to confine a clergyman's cassock. The verb is recorded from 1757 (implied in cinctured).