Why does Paris want to marry Juliet so soon?

To answer this question, take a look at Act IV, Scene I. In this scene, Paris gives two reasons for why he wants to marry Juliet so quickly. First, he tells Friar Lawrence that Juliet's father, Capulet, wants the marriage to happen quickly; Paris does not want to disappoint him.

Second, Paris says that Juliet is still mourning the death of Tybalt and that this is getting in the way of love:

 For Venus smiles not in a house of tears.

Moreover, Paris explains that she is crying too much and he is certain that if they get married, she would feel much better about the situation because she would have a companion, somebody at her side:

Which, too much minded by herself alone,

May be put from her by society.

Once again, Juliet's father also agrees that Juliet is crying too much over Tybalt and that a marriage is the only way to cure her sadness. So, it is important for Paris to not disappoint the man who will be his father-in-law.