How is the theme of love and hate developed in Romeo and Juliet?

Despite its lushly romantic reputation, in Romeo and Juliet love and hate tend to go together. Right from the very moment that Romeo first claps eyes on his beloved Juliet, it's tragically obvious that, if their love is to prevail, it will need to overcome the immense hatred and bitterness that exists between their respective families. Even more tragically, we know from the Prologue that the "star-cross'd lovers" will never be able to achieve this.
Nevertheless, Romeo and Juliet do make a pretty good fist of trying to ensure that love conquers hate. Even as the bodies are piling up around them—with Tybalt and Mercutio two more victims of the long, drawn-out feud between the Montagues and the Capulets, the young lovers are still able to remain true to each other, which, under the circumstances, is a truly remarkable feat.
Yet even so, Romeo himself succumbs to hate when he kills Tybalt in revenge for Mercutio's death. Popular opinion may hold that love and hate are diametrically opposite, but Romeo's killing of Tybalt shows us that there's often a very fine line between them. For in this particular case, Romeo's hatred of Tybalt arises out of his love for his stricken friend Mercutio.