Old English gylt "crime, sin, moral defect, failure of duty," of unknown origin, though some suspect a connection to Old English gieldan "to pay for, debt," but OED editors find this "inadmissible phonologically." The -u- is an unetymological insertion. In law, "That state of a moral agent which results from his commission of a crime or an offense wilfully or by consent" [Century Dictionary], from early 14c. Then use for "sense of guilt," considered erroneous by purists, is first recorded 1680s. Guilt by association recorded by 1919.
"to influence someone by appealing to his sense of guiltiness," by 1995, from guilt (n.). Related: Guilted; guilting. Old English also had a verbal form, gyltan (Middle English gilt), but it was intransitive and meant "to commit an offense, act criminally."