What is Romeo's motivation for killing Tybalt?

Romeo kills Tybalt right after he marries Juliet in Act III. He is now family to Tybalt and does not want to fight him, but he can't tell anyone why. Romeo wasn't ever much of a fighter in the first place, and, due to the Prince's ultimatum from Act I, there are many reasons why Romeo wouldn't want to fight Tybalt. Still, Mercutio engages Tybalt in a duel after Tybalt hurls insult after insult at Romeo. In an effort to stop the fight between Tybalt and Mercutio, Romeo comes between them. Mercutio is fatally wounded because of the interference. A few of Mercutio's last words are directed at Romeo:

"Why the devil came you between us? I was

hurt under your arm" (III.1.99-100).

"A plague o' both your houses!

They have made worms' meat of me. I have it,

And soundly too. Your houses!" (III.1.103-105).

Once Mercutio dies, Romeo feels guilty for having come between his friend and Tybalt in the duel, but he also feels guilty that Mercutio was fighting in his stead. In fact, in a moment of reflection, Romeo thinks he would have been in the right mind to fight his own battle against Tybalt if he weren't so in love with Juliet. Romeo realizes this when saying the following:

"My very friend, that got this mortal hurt

in my behalf; my reputation stain'd

With Tybalt's slander,—Tybalt, that an hour

Hath been my cousin! O sweet Juliet,

Thy beauty hath made me effeminate

And in my temper soft'ned valour's steel! (III.1.107-112).

Romeo believes loving Juliet makes him less of a man to the point that he didn't stand up for himself. Romeo believes Mercutio's death is his fault. His goal then changes from keeping the peace to avenging his best friend. It's as if Mercutio's death awakens a rage inside of Romeo that is unlike his personality and he forgets himself. One might say Romeo suffers from the traumatic event by going crazy for a time. As all reason seems to exit Romeo's mind, he attacks Tybalt with great ferocity. Therefore, Romeo is motivated by his own guilt and Mercutio's death when he goes after Tybalt to kill him.