late 14c., coupen, "to quarrel;" c. 1400, "come to blows, deliver blows, engage in combat," from Old French couper, earlier colper "hit, punch," from colp "a blow" (see coup).
The meaning evolved by 18c. into "handle (successfully), deal with," perhaps influenced by now-obsolete cope "to traffic, bargain for, buy" (15c.-17c.), a word in North Sea trade, from the Flemish version of the Germanic source of English cheap, and compare Copenhagen. Related: Coped; coping.
c. 1200, "large outer garment, cloak, mantle," late 13c. in the specific ecclesiastical sense of "large mantle of silk or other material worn by priests or bishops over the alb on special occasions," from Medieval Latin capa "cloak," from Late Latin cappa (see cap (n.)). It was used figuratively for the "cloak" of night's darkness, from which it was extended to "vault of the sky" in the once-common poetic phrase cope of heaven (late 14c.).