What evidence is there to prove that Friar Lawrence is guilty in Romeo and Juliet?

The clearest piece of evidence to indicate that Friar Laurence is guilty in Shakespeare's Romeo and Juliet is the Friar's own confession in Act 5, scene 3. In his monologue, he confesses that he married the two secretly. He further confesses to giving Juliet the sleeping potion, and says that if he did not, she would have killed herself right there. He confesses to giving a letter to Friar John explaining the plan to Romeo, and that Friar John returned the letter to him undelivered, so that Romeo never knew the contents of the message.

Had he not confessed, the deaths of Romeo and Juliet may have remained a mystery, as Friar Laurence fled from the catacombs before the arrival of the watchmen. Balthasar is found in the churchyard, and might have been implicated if it weren't for the Friar's subsequent confession.

The nurse would have known that the Friar married Romeo and Juliet, but she doesn't know of the plot that the Friar concocts to give Juliet the sleeping potion and alert Romeo, who is banished, so they can sneak away together. Juliet stops confiding in the nurse when the nurse suggests Juliet would be better off marrying Paris.

Without the Friar's confession, there wouldn't be any evidence to prove his guilt. The only witnesses are dead. The letter he penned to Romeo was returned to him by Friar John. If he hadn't had an attack of conscience, he would certainly have gone to his grave without anyone knowing the depth of his involvement.