early 14c., avantage, "position of being in advance of another," from Old French avantage "advantage, profit, superiority," from avant "before," probably via an unrecorded Late Latin *abantaticum, from Latin abante (see advance).
The -d- is a 16c. intrusion on the analogy of Latin ad- words. Meaning "a favoring circumstance" (the opposite of disadvantage) is from late 15c. Tennis score sense is from 1640s, first recorded in writings of John Milton, of all people. Phrase to take advantage of is first attested late 14c.