Is it farther or further?
late 12c., "God's favor or help," from Old French grace "pardon, divine grace, mercy; favor, thanks; elegance, virtue" (12c.), from Latin gratia "favor, esteem, regard; pleasing quality, good will, gratitude" (source of Italian grazia, Spanish gracia), from gratus "pleasing, agreeable," from PIE root *gwere- "to favor" (cf. Sanskrit grnati "sings, praises, announces," Lithuanian giriu "to praise, celebrate," Avestan gar- "to praise").
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. The short prayer that is said before or after a meal (early 13c.; until 16c. usually graces) has a sense of "gratitude."
c.1200, "to thank," from Old French gracier, from grace (see grace (n.)). Meaning "to show favor" (mid-15c.) led to that of "to lend or add grace to something" (1580s, e.g. grace us with your presence), which is the root of the musical sense in grace notes (1650s). Related: Graced; gracing.
Greek and Roman goddesses of loveliness and charm. According to most stories, there were three of them. They were supposed to be invited to every banquet.
(1.) Of form or person (Prov. 1:9; 3:22; Ps. 45:2). (2.) Favour, kindness, friendship (Gen. 6:8; 18:3; 19:19; 2 Tim. 1:9). (3.) God's forgiving mercy (Rom. 11:6; Eph. 2:5). (4.) The gospel as distinguished from the law (John 1:17; Rom. 6:14; 1 Pet. 5:12). (5.) Gifts freely bestowed by God; as miracles, prophecy, tongues (Rom. 15:15; 1 Cor. 15:10; Eph. 3:8). (6.) Christian virtues (2 Cor. 8:7; 2 Pet. 3:18). (7.) The glory hereafter to be revealed (1 Pet. 1:13).