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.

He pretends an interest. https://dictionary.cambridge.org/dictionary/english/affect

Chris’ answer is correct. Another use is with accents. “He can affect a pretty decent French accent” (He speaks in a way that makes him sound like a French speaker. This use is a little more colloquial than “affecting an interest” where we would typically use a construction with “pretend” in speech)

In this context, "affects" means that he 'has' an interest in the arts.