quit (v.) Look up quit at Dictionary.com
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.) Look up quit at Dictionary.com
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.)).