Paris represents coming-of-age in “Romeo and Juliet” because he is the man that Juliet's father has chosen for Juliet to marry. She is now (just) old enough to be married, at not-quite-14, and custom dictates that she is not only expected to get married as soon as possible (even Lord Capulet has reservations about that), but expected to marry somebody that her father has chosen. Paris is often portrayed as older than Juliet; although the text doesn’t specify his age precisely, he is old enough to negotiate with Lord Capulet on his own and so could be said to represent the “adult” world that Juliet is very close to joining. Some productions cast Paris significantly older, closer in age to Lord Capulet himself, a middle-age man looking for a wife young enough to have children, as a way of further emphasizing the idea of an “adult” world and making the possibility of marriage with him that much more horrifying to Juliet. Paris represents the life that awaits her if she's a “good” daughter who does what her father commands. It’s the world of the “good” daughter that she rebels against in the play, choosing Romeo or even death rather than Paris.