Why does Paris want to marry Juliet so soon?
In Act IV, scene i, Paris explains to Friar Laurence his rush to marry Juliet. He says it's because she is grieving too much over her cousin Tybalt's death. She has been spending too much time alone. Juliet's father, Paris says, thinks so much grief is unhealthy, and that a wedding—and a companion to be with—will help her to recover her equilibrium. Love, however, is not the primary motivation at the moment, at least not on Juliet's part, because, as Paris puts it, a person in mourning can't fall in love ("Venus smiles not in a house of tears"). He says,
Immoderately she weeps for Tybalt’s death,And therefore have I little talked of love,For Venus [love] smiles not in a house of tears.Now, sir, her father counts it dangerousThat she do give her sorrow so much sway,And in his wisdom hastes our marriageTo stop the inundation of her tears—
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.