mid-13c., "abundance; as much as one could desire; an ample supply," from Old French plentee, earlier plentet "abundance, profusion" (12c., Modern French dialectal plenté), from Latin plenitatem (nominative plenitas) "fullness," from plenus "full, filled, greatly crowded; stout, pregnant; abundant, abounding; complete," from PIE root *pele- (1) "to fill."
From early 14c. as "a large amount, a great deal." The meaning "condition of general abundance" is from late 14c. The colloquial adverb meaning "very much" is first attested 1842. Middle English had parallel formation plenteth, from the older Old French form of the word.
word-forming element attached to nouns (and in modern English to verb stems) and meaning "full of, having, characterized by," also "amount or volume contained" (handful, bellyful); from Old English -full, -ful, which is full (adj.) become a suffix by being coalesced with a preceding noun, but originally a separate word. Cognate with German -voll, Old Norse -fullr, Danish -fuld. Most English -ful adjectives at one time or another had both passive ("full of x") and active ("causing x; full of occasion for x") senses.
It is rare in Old English and Middle English, where full was much more commonly attached at the head of a word (for example Old English fulbrecan "to violate," fulslean "to kill outright," fulripod "mature;" Middle English had ful-comen "attain (a state), realize (a truth)," ful-lasting "durability," ful-thriven "complete, perfect," etc.).