check (v.1)youdaoicibaDictYouDict[check 词源字典]
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.1). 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 etymology, check origin, 英语词源]
resign (v.)youdaoicibaDictYouDict
late 14c., "give up, surrender, abandon, submit; relinquish," from Old French resigner "renounce, relinquish" (13c.), from Latin resignare "to check off, annul, cancel, give back, give up," from re- "opposite" (see re-) + signare "to make an entry in an account book," literally "to mark" (see sign (v.)).

The sense is of making an entry (signum) "opposite" -- on the credit side -- balancing the former mark and thus canceling the claim it represents. The specific meaning of "give up a position" is first recorded late 14c. Sense of "to give (oneself) up to some emotion or situation" is from 1718. Related: Resigned; resigning.