It's true R&J both come from "affluent families, but I'd like to point out that these families are not royalty, but merchants. Why is this important? Aristotle's Poetics says that tragic characters must come from families of kings and queens (or words to the same effect). If you think of it, Hamlet is a prince, Macbeth is a king, etc. Some people think that this is among several "definitions" or "rules" of tragic plays. I think it is much more likely that he is describing plays written for two festivals in which playwrights competed for prizes, and that those plays had certain rules.
I think Romeo and Juliet is a tragedy. Scholars, however, usually call it a "domestic tragedy," that is one which describes the suffering of characters who are not members of ruling families. If you think about it, Othello is also such a play. There are three or four other plays which survive from Shakespeare's time which are more like R&J and Othello than like Hamlet or King Lear.
I think the "tragedy" is no less sad or effecting in these plays. If you think about it, Death of a Salesman is also such a play. Miller devotes a lot of speeches comparing Willie Loman to great tragedies of the past. I think a dandy paper could be written, after a good bit of research, about this whole concept.