late 12c., "God's unmerited favor, love, or help," from Old French grace "pardon, divine grace, mercy; favor, thanks; elegance, virtue" (12c., Modern French grâce), from Latin gratia "favor, esteem, regard; pleasing quality, good will, gratitude" (source of Italian grazia, Spanish gracia; in Church use translating Greek kharisma), from gratus "pleasing, agreeable," from PIE *gwreto-, suffixed form of root *gwere- (2) "to favor."
Sense of "virtue" is early 14c., that of "beauty of form or movement, pleasing quality" is mid-14c. In classical sense, "one of the three sister goddesses (Latin Gratiæ, Greek Kharites), bestowers of beauty and charm," it is first recorded in English 1579 in Spenser. In music, "an embellishment not essential to the melody or harmony," 1650s. As the name of the short prayer that is said before or after a meal (early 13c.; until 16c. usually graces) it has a sense of "gratitude." As a title of honor, c. 1500.
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.).