Good gentle youth, tempt not a desperate man, fly hence and leave me, think upon these gone.
Condemned villain, I do apprehend thee. Obey and go with me; for thou must die!
Will thou provoke me? Then have at thee boy!
I do defy thy conjurations, and apprehend thee for a felon here!
In faith I will. Let me peruse this face.. That knight who wooed fair Juliet, I'll bury thee in a triumphant grave.
OH! I am slain, if thou be merciful. Open the tomb, lay me with Juliet.
Romeo was reaching into Juliet's tomb, and that is when Paris had caught him. Since Paris is also in love with Juliet, he got angry at Romeo, and Romeo was trying to get Paris to be calm because he was claiming that he was not doing anything wrong.
Then, their "argument" turned into a fight. They got too angry with each other which caused things to get out of hand.
The two took out all of their anger out on each other, that Romeo had ended up murdering Paris with the sword. Once Paris was slowly dying, he told Romeo to lay him in the tomb with Juliet.