Remember that Romeo and Juliet just met for the first time the previous day. Until that time, he was infatuated with another woman. Juliet is also the daughter of his sworn enemy. It is understandable that he would be a bit hesitant in entering into a new and rapidly progressing relationship.
In lines 9-15, the friar has just warned Romeo that this relationship could easily be doomed to failure. Romeo trusted the friar and would surely have been shaken by such a strong speech. This is only the third time Romeo has spoken to Juliet (first at the party and second in the garden/balcony). It makes sense that he would want some reassurance that she does love him before they get married.
If you recall Romeo and Juliet's previous conversation from act II scene ii, Romeo states he has doubts about their relationship because it is "too flattering-sweet to be substantial." with all the obstacles to such a marriage, we might think less of Romeo's intelligence had he not asked for a little reassurance.