quityoudaoicibaDictYouDict[quit 词源字典]
quit: [13] Quit comes from the same ultimate source as quiet – Latin quiētus. This originally meant simply ‘quiet, calm’, but in medieval Latin it developed a wider range of senses, including ‘unharmed’ and ‘free’. From it was derived the verb quiētāre ‘set free, discharge’, which reached English via Old French quiter. The derived forms acquit and requite [16] come from the same source, and quite is essentially the same word as quit.
=> quiet[quit etymology, quit origin, 英语词源]
quit (v.)youdaoicibaDictYouDict
c. 1200, "to repay, discharge" (a debt, etc.), from Old French quiter "clear, establish one's innocence;" also transitive, "release, let go, relinquish, abandon" (12c.), from quite (see quit (adj.)).

Meaning "to reward, give reward" is mid-13c., that of "take revenge; to answer, retort" and "to acquit oneself" are late 14c. From c. 1300 as "to acquit (of a charge), declare not guilty." Sense of "leave, depart" is attested from c. 1400; that of "stop" (doing something) is from 1640s. Meaning "to give up, relinquish" is from mid-15c. Related: Quitted; quitting. Quitting time is from 1835.
quit (adj.)youdaoicibaDictYouDict
c. 1200, "free, clear" (of debt, etc.), from Old French quite, quitte "free, clear, entire, at liberty; discharged; unmarried," from Medieval Latin quitus, quittus, from Latin quietus "free" (in Medieval Latin "free from war, debts, etc."), also "calm, resting" (see quiet (adj.)).