check (n.1) Look up check at Dictionary.com
c.1300, "a call in chess noting one's move has placed his opponent's king (or another major piece) in immediate peril," from Old French eschequier "a check at chess" (also "chess board, chess set"), from eschec "the game of chess; chessboard; check; checkmate," from Vulgar Latin *scaccus, from Arabic shah, from Persian shah "king," the principal piece in a chess game (see shah; also compare checkmate (n.)). Also c.1300 in a generalized sense, "harmful incident or event."

When the king is in check that player's choices are severely limited. Hence, "sudden stoppage" (early 14c.), and by c.1700 to "a token of ownership used to check against, and prevent, loss or theft" (surviving in hat check) and "a check against forgery or alteration," which gave the modern financial use of "bank check, money draft" (first recorded 1798 and often spelled cheque), probably influenced by exchequer. Checking account is attested from 1897, American English. Blank check in the figurative sense attested by 1849. Checks and balances is from 1782, perhaps originally suggesting machinery.
check (v.1) Look up check at Dictionary.com
late 15c., in chess, "to attack the king; to put (the opponent's king) in check;" earlier (late 14c.), "to stop, arrest; block, barricade;" see check (n.).

A player in chess limits his opponent's ability to move when he places his opponent's king in check. All the other senses seem to have developed from the chess sense: "To arrest, stop;" then "to hold in restraint" (1620s); and finally "to hold up or control" (an assertion, a person, etc.) by comparison with some authority or record, 1690s.

Hence, to check off (1839); to check up (1889); to check in or out (in a hotel, of a library book, etc., by 1918). To check out (something) "to look at, investigate" is from 1959. Related: Checked; checking.
check (v.2) Look up check at Dictionary.com
"mark like a chessboard, incise with a pattern of squares or checks," late 14c. (implied in checked), from check (n.1). Related: Checking.
check (n.2) Look up check at Dictionary.com
"pattern of squares, cross-like pattern," c.1400, short for checker (n.1).