PARIS: Tristan asking me out? Why would he do that?
RORY: Why would he not do that?
PARIS: Because he’s gorgeous and experienced and only dates those most likely to become a trophy wife.
Trophy wife is the term for a woman believed to be only chosen by her wealthy husband as a status symbol, usually because she’s young(er) and attractive. It is derogatory to both people in the marriage; the inference being that the man can only attract women because of his money, and that the woman has nothing to offer except her appearance. The term dates to perhaps the 1950s, but became popularised in the 1980s.