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."
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.
as an insult, "one who shirks or gives up," by 1878, American English, in reference to race horses, agent noun from quit (v.) in the "stop, cease" sense. It is attested by 1871 as "one who gives up (chewing tobacco)."
"on even terms with one another," in to be quits (with one) "have made a mutual satisfaction of claims or demands," 1660s; earlier "discharged of a liability" (c. 1200), perhaps from Medieval Latin quittus (see quit (adj.)). An adjective used as a quasi-noun in plural form. Quit (adj.) "satisfied" is attested from c. 1400.
c. 1300, "completely, altogether, entirely, wholly," adverbial form of Middle English quit, quite (adj.) "free, clear" (see quit (adj.)). Originally "thoroughly;" the weaker sense of "fairly" is attested from mid-19c. For quite a few, etc., see few (adj.). In Middle English the adverb also could be quitely, quitelich, quitli (c. 1300).
It forms all or part of: acquiesce; acquit; awhile; coy; quiesce; quiescent; quiet; quietism; quietude; quietus; quit; quitclaim; quite; quit-rent; quittance; requiescat; requiem; requite; while; whilom.
It is the hypothetical source of/evidence for its existence is provided by: Avestan shaitish "joy," shaiti- "well-being," shyata- "happy;" Old Persian šiyatish "joy;" Latin quies "rest, repose, quiet;" Old Church Slavonic po-koji "rest;" Old Norse hvild "rest."