Romeo and Juliet as a play uses the themes of love and hate to demonstrate the power of relationships.
Under the circumstances of their forbidden love and the results of the secrecy that ensued, many sub-conflicts play out to complicate matters. This play is identified as a tragedy and rightly so. A hate so deeply embedded had a chance at love and the Prince even comments in the end to both Montague and Capulet about the potential for love their families had. But alas, hate resulted in tremendous death.
Romeo's love is so clearly expressed with deep emotion and instant loyalty. In the balcony scene, he commits to her immediately. As for hate, you only see that reveal itself when those to whom he is loyal are hurt: so, he killed Tybalt for killing Mercutio
Juliet falls just as hard but not as openly. As Romeo had tripped upon her thoughts, she felt she had to be guarded about her feelings for him. Her hate is seldom expressed, if ever.
Mercutio definitely takes side with the Montagues, but being a kinsman of the Prince, maybe he shouldn't take sides. He does utter a curse in his last words to both houses to demonstrate his feeling about their feud.
Tybalt is all hate. We don't see him deal anywhere in between. Perhaps this is to be a foil to Romeo?
Hope this helps.
I would say that Romeo and Juliet's characters are defined by love and by hate. They are defined by their love for each other, but they are also defined from the outside by their families' hate. (I mean that this hate defines their identities even though they do not want it to.)
By contrast, Tybalt's character (or what we see of it), is completely dominated by hate. Perhaps more than any other character, he typifies the problems the Montagues and Capulets have. He wants to confront Romeo at the dance, he wants to fight Mercutio and Romeo on the street. We really don't see him having any other side to him than this hate.
Mercutio does not seem to be as consumed by hate (his personality seems dominated by the desire for fun) but he is quick to want to fight Tybalt and this causes his death as well.