In Romeo and Juliet, what is the county Paris doing in Juliet's tomb when Romeo arrives?

Paris' visit occurs in scene 3 of Act 5. Juliet has been interred in the family tomb since it is believed that she is dead. The county Paris, who had been prepared for a wedding, had to quickly adjust from one who was to undertake nuptials to one who had to mourn. His happiness had turned to sadness. He had arrived at the burial vault, accompanied by his page who he asked to keep watch, in the dark of night.

He gives a reason for his visit:

Sweet flower, with flowers thy bridal bed I strew,--
O woe! thy canopy is dust and stones;--
Which with sweet water nightly I will dew,
Or, wanting that, with tears distill'd by moans:
The obsequies that I for thee will keep
Nightly shall be to strew thy grave and weep.

He is carrying flowers to place on Juliet' grave, for he believes her to be deceased. He promises to water the flowers inside her burial chamber every night or, failing that, to water it with tears of loss and grief. He mentions that he will perform these rites every night and weep. It is obvious that Paris had fallen in love with Juliet and was deeply saddened by her untimely demise. His nightly visits would be symbolic of his dedication and love for her.

It is tragically ironic that Paris' act of love culminates in his death, for Romeo arrives soon after and when Paris sees him, attempts to arrest someone whom he sees as a criminal since Romeo had been banished. He thinks that Romeo is there to defile the grave. The two men start fighting and Paris is mortally wounded.

Before he dies, he lodges the following request:

If thou be merciful,
Open the tomb, lay me with Juliet.

Further irony also lies in the fact that Juliet is not actually dead. In her and friar Laurence's plan to avoid her marrying Paris and being reunited with Romeo, they had decided that she should drink a potion which would put her in a death-like sleep. Her parents would then obviously believe that she has died and entomb her in the family vault. Juliet would then later wake from her deep slumber and the friar and Romeo would be there to whisk her away. She would then be with her true love and her parents would be none the wiser.

Unfortunately, things ultimately and tragically turn out to not work as planned.