If I remember right, Romeo just secretly married Juliet. And since Tybault's now "family" he doesn't want to fight him.

Romeo had just married Juliet, Tybalt's kinsman, thus becoming Tybalt's kinsman. He didn't want to fight his kinsman, even if that kinsman didn't know they had just recently become related.

Well Romeo just secretly married Juliet, who is Tybalt's cousin, so Romeo doesn't want to fight with him because they are know cousin in-law's.