You need to look in particular at Act II scene 3 to find the answer to this question. This scene comes straight after the famous balcony scene of scene 2 where Romeo and Juliet pledge their love to each other, but in scene 3 we see Romeo trying to explain his change of heart to Friar Lawrence, and talking about what has happened to him.
Obviously it is very suspicious that Romeo, having been so "love-sick" for Rosaline, now says
I have forgot that name and that name's woe
Of course, when Romeo tells Friar Lawrence about the new object of his affections, the Friar is harshly critical:
Holy Saint Francis! What a change is here!
Is Rosaline, that thou didst love so dear,
So soon forsaken? Young men's love then lies
Not truly in their hearts, but in their eyes.
Romeo responds talking about the difference between his love for Rosaline and his new love for Juliet:
Her I love now
Doth grace for grace and love for love allow.
The other did not so.
Romeo thus says that a key difference in his relationship with Juliet is that there is a mutual love and favour. As Friar Lawrence said, he "doted" on Rosaline, and didn't love her, which suggests that he was too infatuated and it wasn't a relationship where both parties had equal love and respect. It is this love that makes Romeo grow up and mature and try to seek a more peaceful course in life, trying to avoid battle and bloodshed.