1610s, "loose outer garment" (worn by men in Eastern countries or in ancient times), from French veste "a vest, jacket" (17c.), from Italian vesta, veste "robe, gown," from Latin vestis "clothing," from vestire "to clothe" (from PIE *wes- (2) "to clothe," extended form of root *eu- "to dress"). The sleeveless garment worn by men beneath the coat was introduced by Charles II in a bid to rein in men's attire at court, which had grown extravagant and decadent in the French mode.
The King hath yesterday, in Council, declared his resolution of setting a fashion for clothes .... It will be a vest, I know not well how; but it is to teach the nobility thrift. [Pepys, "Diary," Oct. 8, 1666]
Louis XIV of France is said to have mocked the effort by putting his footmen in such vests.