c. 1300, in chess, "a call 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, hostile environment."
As "an exposure of the king to a direct attack from an opposing piece" early 15c. When his king is in check, a player's choices are severely limited. From that notion come the many extended senses: From the notion of "a sudden stoppage, hindrance, restraint" (1510s) comes that of "act or means of checking or restraining," also "means of detecting or exposing or preventing error; a check against forgery or alteration."
Hence: "a counter-register as a token of ownership used to check against, and prevent, loss or theft" (as in hat check, etc.), 1812. Hence also the financial use for "written order for money drawn on a bank, money draft" (1798, often spelled cheque), which was probably influenced by exchequer. Hence also "mark put against names or items on a list indicating they have been verified or otherwise examined" (by 1856).
From its use in chess the word has been widely transferred in French and English. In the sense-extension, the sb. and vb. have acted and reacted on each other, so that it is difficult to trace and exhibit the order in which special senses arose [OED]
The meaning "restaurant bill" is from 1869. Checking account is attested from 1897, American English. Blank check in the figurative sense is attested by 1849 (compare carte blanche). Checks and balances is from 1782, perhaps originally suggesting machinery.