Yours, Etc.: Origins and Uses of 8 Sign-Offs
"freed, exonerated," 1670s, past participle adjective from acquit (v.). Formerly in this sense was acquit (late 14c.), perhaps on analogy of pps. such as hit.
early 13c., "to satisfy a debt" (either for oneself or on behalf of another), from Old French aquiter "pay, pay up, settle a claim" (12c.), from à "to" (see ad-) + quite "free, clear" (see quit (adj.)). Meanings "set free from charges" and "to discharge one's duty" both recorded from late 14c. Related: Acquitted; acquitting.