If I say that Romeo is to blame for Juliet's death how can I prove it with evidence?

One might argue that Romeo is responsible for Juliet's death for three reasons. First, he ignores the advice of Friar Laurence and rushes into his relationship with Juliet. Second, he fails to fully consider Juliet when he fights Tybalt to the death in Act III, Scene 1. Third, he impetuously launches into his quest to commit suicide before thinking to consult Friar Laurence, who has been a friend and loyal advisor in the past.

In Act II, Scenes 3 and 6, Friar Laurence counsels Romeo to not be so impatient and to ease into his love for Juliet. He tells Romeo in Scene 3, "Wisely and slow. They stumble that run fast." Again in Scene 6, he repeats these feelings just before he marries the two young lovers:

Therefore love moderately. Long love doth so.
Too swift arrives as tardy as too slow.

The Friar's words, however, fall on deaf ears as Romeo is quick to marry, quick to seek revenge against Tybalt and quick to do away with himself when he thinks Juliet is dead.

In the street fight in Act III, Scene 1, after Mercutio is killed, Romeo believes he has been "effeminate" and blindly flies into a rage, challenging Tybalt, who inexplicably has returned to the scene. Even though the Prince has proclaimed that he would enforce the death penalty for any who engaged in fighting, Romeo ignores this, as well as his obligations to his new bride. After killing Tybalt, he realizes the situation and claims he is "Fortune's fool." Throughout the play, Romeo seems the victim of fate, yet each step he takes is of his own volition.

This is clear in the final Act when he immediately plots his own suicide after hearing the mistaken news from Balthasar that Juliet is dead. He even believes he is going against fate in procuring poison and rushing off to the tomb: "Is it e’en so?—Then I deny you, stars!" In reality, he is playing into fate and proceeding on a course which means not only his doom but also Juliet's. If he had simply taken a little time to ascertain the situation and sought out the Friar for advice, he would have known that Juliet wasn't dead and that his intentions were foolish. Unfortunately for Juliet, Romeo is at his most impulsive when she needs him to be mature and calculating.