Juliet is quite young in this story. And, the nurse has raised her from an infant. The nurse probably knows Juliet better than her own parents as the custom was to have babies and then give them to wet-nurses to be raised until they were old enough to participate in the family business. Since Juliet is a girl, the only thing she can do is marry well to someone that will help the Capulets prosper. We are not told how old Paris is, but we can assume that he is quite a bit older than Juliet and someone her father knows well. This is not necessarily going to make a good match for Juliet, and the nurse knows Juliet's heart is taken by Romeo.
In the end, the nurse caves in under pressure from the family and in Romeo's absence, she tells Juliet to marry Paris. I think the Nurse had hopes that the Montague and Capulet families would be on friendly terms once the children's marriage was made public, but it was done in secret and without the proper banns being said. It could be argued that the marriage was not legitimate. And, in Romeo's absence, he is useless to Juliet. It would be better for her to be married quickly to Paris just in case she had conceived during her intimate night with Romeo.
It is also possible that the nurse was using the entire situation to "get at" the Capulets for any possible mistreatment of her during her employment with them.
The Nurse loves Juliet and has taken care of her since childhood. Therefore, it is only natural that the Nurse would want Juliet to be happy. Despite Romeo’s family background, the Nurse sees that he is attractive and that he obviously loves Juliet as well. The Nurse also knows that Juliet’s father plans to marry Juliet off to Count Paris against her will, so helping Romeo and Juliet elope will foil that outcome. Finally, the Nurse may well be influenced by the Priest. Clergy were influential figures, and since the Priest is willing to help the young couple elope, his willingness may have convinced the Nurse that it is a good idea.