quite adv.

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."

Old English feawe (plural; contracted to fea) "not many, a small number; seldom, even a little," from Proto-Germanic *fawaz (source also of Old Saxon fa, Old Frisian fe, Old High German fao, Old Norse far, Danish faa), from PIE root *pau- (1) "few, little."

Always plural in Old English, according to OED "on the analogy of the adverbial fela," meaning "many." Phrase few and far between attested from 1660s. Unusual ironic use in quite a few "many" (1854), earlier a good few (1803).

There is likewise another dialectical use of the word few among them [i.e. "the Northern Counties"], seemingly tending to its total overthrow; for they are bold enough to say—"a good few," meaning a good many. [Samuel Pegge, "Anecdotes of the English Language," London, 1803]

*kweiə-, also *kwyeə-, Proto-Indo-European root meaning "to rest, be quiet."

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."