What are the circumstances surrounding the death of Paris?

The death of Paris occurs in Act V scene 3 of this great
tragedy. In this scene, we see a grief-stricken Paris at Juliet's tomb, pledging to
attend his dead fiancee's tomb every night and "dew" it with his tears every night.
However, the boy he has with him whistles to indicate that somebody is coming, and so he
retires before Romeo enters. When Paris sees Romeo opening the tomb, he re-enters the
stage to apprehend Romeo and get his revenge on him for killing Tybalt and making Juliet
suffer so badly with grief. Note how Paris addresses
Romeo:

Stop
thy unhallowed toil, vile Montague!

Can vengeance be
pursued further than death?

Condemned villain, I do
apprehend thee.

Obey, and go with me, for thou must
die.

Unfortuanately, Paris
hasn't counted on the fact that Romeo has come here precisely so that he can die, and
the insistence of Paris that he must apprehend Romeo leads to the two of them fighting,
even though Romeo tells Paris that he loves Paris better than he does
himself:

By
heaven, I love thee better than myself,

For I come hither
armed against myself.

Stay not, be gone. Live, and
hereafter say

A madman's mercy bid thee run
away.

In spite of Romeo's
words, Paris insists on trying to capture Romeo and prevent him from going into the tomb
and doing whatever he was planning on doing, and so Romeo is forced to kill Paris so
that he can enter the tomb of his beloved and die with her
there.