cross-check (n.)

c. 1400, "to the side," from on cros, variant of across, and in part from cross (adj.). From c. 1600 as "in an adverse way."

late 15c., in chess, "to attack the king; to put (the opponent's king) in check;" earlier (late 14c.) in a figurative sense, "to stop, arrest; block, barricade;" from check (n.1) or Old French eschequier, from the noun in French. A player in chess limits his opponent's ability to move when he places his opponent's king in check.

The other senses seem all to have developed from the chess sense, or from the noun: "To arrest, stop," then "to hold in restraint" (1620s); "to hold up or control" (an assertion, a person, etc.) by comparison with some authority or record (1690s); of baggage, etc., "to hand over in return for a check that serves as a means of identifying" (1846); "to note with a mark as having been examined, etc., mark off from a list" (1928).

Hence, to check off (1839); to check up (1883); to check in or out (in a hotel, of a library book, etc., 1909). To check out (something) "to look at, investigate" is from 1959. Related: Checked; checking.