"legal settlement" of a debt, obligation, etc., early 14c., aquitaunce, from Old French aquitance and Medieval Latin acquietantia; see acquit + -ance.
Entries linking to acquittance
acquit v.
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 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.
-ance
word-forming element attached to verbs to form abstract nouns of process or fact (convergence from converge), or of state or quality (absence from absent); ultimately from Latin -antia and -entia, which depended on the vowel in the stem word, from PIE *-nt-, adjectival suffix.
Latin present-participle endings for verbs stems in -a- were distinguished from those in -i- and -e-. Hence Modern English protestant, opponent, obedient from Latin protestare, opponere, obedire.
As Old French evolved from Latin, these were leveled to -ance, but later French borrowings from Latin (some of them subsequently passed to English) used the appropriate Latin form of the ending, as did words borrowed by English directly from Latin (diligence,absence).
English thus inherited a confused mass of words from French (crescent/croissant), and further confused it since c. 1500 by restoring -ence selectively in some forms of these words to conform with Latin. Thus dependant, but independence, etc.