to become (a state, condition, etc.)
「付く」 has another reading with different meanings.
高校生になって彼は最近色気付いてきた。
Recently he's becoming aware of romance.
歳を取って最近、年寄り付いてきたなあ。
Recently, I've been feeling my age.
息子も高校生になって男らしく付いたものだ。
My son has become manly now that he's in high school.