This is a much less common use of "affect". Here, it means "pretends to have, in order to impress people" He is not actually interested in art, he just wants people to think that he is interested in art.
"Bob is actually middle-class, but he affects great wealth ( =he pretends to be very wealthy) in order to make friends with wealthy people."
"Affect" is only used this way in very advanced writing. We don't use "affect" this way in daily speech.