mid-13c., aquiten, "repay, reciprocate, reward or retaliate for" (a good or bad deed); c. 1300 as "satisfy a debt; redeem (a pledge)," from Old French aquiter, acquiter "pay, pay up, settle a claim" (12c., Modern French acquitter), from a- "to" (see ad-) + quite "free, clear," 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"). Also in part from Medieval Latin acquitare.
From mid-14c. as "relieve (someone) of an obligation, release from a pledge," hence the meanings "set (an accused person) free from charges, pronounce not guilty," and "discharge one's duty; behave or conduct oneself" (for better or worse), all of which date to the late 14c. The notion in the word is "to release or discharge," from an obligation or from accusation, guilt, censure, or suspicion. Related: Acquitted; acquitting.
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."
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.
"remission, forgiveness," c. 1200, from Old French absolucion, earlier assolucion, from Latin absolutionem (nominative absolutio) "completion, acquittal," noun of action from past-participle stem of absolvere "set free, loosen, acquit," from ab "off, away from" (see ab-) + solvere "to loosen, dissolve; untie, release; dismiss," from PIE *se-lu-, from reflexive pronoun *s(w)e- (see idiom) + root *leu- "to loosen, divide, cut apart." Originally of sins; in general use from c. 1400.
early 14c., relēs, "abatement of distress; means of deliverance," from Old French relais, reles (12c.), a back-formation from relesser, relaissier "to relinquish, quit, let go, leave behind, abandon, acquit" (see release (v.)). In law, mid-14c., "transferring of property or a right to another;" late 14c. as "release from an obligation; remission of a duty, tribute, etc."
In archery, the meaning "act and manner of releasing" (a bow, etc.) is from 1871. The sense of "action of publication" is from 1907; as "a news item or official statement (to the press)" is by 1927. The meaning "action of making a film available to theaters" is from 1912, later of musical recordings, etc. The sense of "written authorization or permission for publication" is by 1965.
However eslegier meant "acquit, clear of charges in a lawsuit," and the Middle English word somehow acquired the meaning of French alléguer, from Latin allegare/adlegare "send for, bring forth, name, produce in evidence, send on business," from ad "to" (see ad-) + legare "to depute, send" (see legate). Related: Alleged; alleging.