In the fourteenth century of Italy, as patrician families looked to other families of nobility for both political and financial alliances, for Lord Capulet, the marriage of his daughter to Paris, a kinsman of the Prince of Verona, would be an advantageous arrangement for the feuding Capulets. While there is no documentation of this idea in the play, one wonders why Paris approaches Lord Capulet with his proposal, but it does follow in the next scene after the Prince's "Rebellious subjects" speech in which he threatens the feuding Capulets and Montagues "on pain of death" to not disturb the streets of Verona that Lord Capulet would listen to Paris. In addition, Paris may believe that such an alliance between his family and the Capulets would ameliorate some of the tensions, too.
However, in Act I, Scene 2, Capulet is not eager to give away his daughter at such a young age, although he encourages Paris, who finds Juliet desirable in beauty and in nobility, to "woo her,"
My child is yet a stranger in the world--
....And too soon marred are those so early made.
The earth hath swallowed all my hopes but she....
But woo her, gentle Paris, get her heart.
My will to her consent is but a part;
An' she agree within her scope of choice..... (1.2.8-18)
Of course, Lord Capulet changes his mind when he fears that Juliet contemplates something rash in her terrible grief for Tybalt, for he considers marriage to Paris safer than what Juliet may do.
Juliet would be a wonderful trophy wife for him. She is young, beautiful, and a virgin. Paris even says, "Happier than she are younger mothers made." (Act I). This suggests that he really desires a young wife. Also, Juliet comes from a wealthy family and that would be beneficial for Paris as well since that would mean a larger dowry for him.