c. 1200, quiten, "to repay, discharge" (a debt, claim, etc.), from Old French quiter "to clear, establish one's innocence;" also transitive, "release, let go; absolve, relinquish, abandon" (12c., Modern French quitter), from quite "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" (from PIE root *kweie- "to rest, be quiet").
Meaning "to reward, give reward, repay" is from 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 "to leave, depart from, go away from" is attested by late 14c.; that of "stop, cease" (doing something) is from 1640s. Meaning "to give up, relinquish" is from mid-15c. Related: Quitted; quitting. Quitting time "time at which work ends for the day" is from 1835.
