This is an interesting question. Shakespeare wants to build tension, so he has many people show up at the Capulet tomb perhaps creating a stronger sense of hope that the "tragedy" fortold in the prologue can be avoided and that Juliet will indeed be rescued by Romeo and swept away to live happily ever after.
The Friar arrives in order to comfort Juliet in the event that Romeo is late in coming to take her away. He has an ulterior motive in protecting his reputation as a Friar and also because he married the two in secret which probably will not be looked on favorably by either of the two affluent families.
Paris is there to genuinely mourn his fiancee who was taken from him before their scheduled wedding. Both he and Romeo have a "claim" to Juliet. Both are angry when they find the other in her tomb.
It's all in the name of suspense...Shakespeare unfolds it carefully for all of us to hope against what we know is going to happen...to have us sitting on the edge of our seats to the final moment when they are both discovered dead and the families bury their only children and with them their feud.