quit (adj.)
c. 1200, "excused, exempt, free, clear" (of debt, obligation, penalty, etc.), from Old French quite , quitte "free, clear, entire, at liberty; discharged; unmarried," and directly 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").
From mid-13c. as "deprived of." From c. 1300 of real property, "exempt from taxes or other dues or claims."
also from
c. 1200
quit (v.)
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."