Why was Romeo interested in Juliet?

This question is unclear as to whether it is asking about Romeo's initial interest in Juliet or his continued interest by the end of the play.  I will focus my answer on his initial interest.  

I think Romeo is initially interested in Juliet because he finds her really attractive.  Some people would argue that Romeo's first glimpse of Juliet is evidence for love at first sight.  What the text indicates is that Romeo is immediately...

This question is unclear as to whether it is asking about Romeo's initial interest in Juliet or his continued interest by the end of the play.  I will focus my answer on his initial interest.  

I think Romeo is initially interested in Juliet because he finds her really attractive.  Some people would argue that Romeo's first glimpse of Juliet is evidence for love at first sight.  What the text indicates is that Romeo is immediately attracted to Juliet based solely on her appearance.  He says that she is too beautiful for this world and far outshines the beauty of any other woman.  

Oh, she doth teach the torches to burn bright!

It seems she hangs upon the cheek of night

Like a rich jewel in an Ethiope’s ear,

Beauty too rich for use, for earth too dear.

So shows a snowy dove trooping with crows

As yonder lady o'er her fellows shows.

Romeo is so taken by her enchanting beauty that he even questions whether or not he truly loved anybody before setting his eyes upon the beauty that is Juliet.

Did my heart love till now? Forswear it, sight!

For I ne'er saw true beauty till this night.

He walks over to Juliet, they say a total of 14 lines, and then they begin kissing. Many audience members find this sequence quite endearing, but I tend to be a bit of a cynic when it comes to Romeo.  I think a lot of his interest in Juliet is based on the fact that Romeo loves the idea of being in love with somebody very attractive.  Keep in mind that just a few scenes before Romeo sees Juliet, he is completely heartbroken over the fact that Rosaline does not "love" him back the way that he loves her.  

Well, in that hit you miss. She'll not be hit
With Cupid's arrow. She hath Dian's wit,
And, in strong proof of chastity well armed,
From love's weak childish bow she lives unharmed.
She will not stay the siege of loving terms,
Nor bide th' encounter of assailing eyes,
Nor ope her lap to saint-seducing gold.

Even in spite of the fact that Rosaline does not love him back, Romeo wholeheartedly believes that he will never be able to find a love as great as Rosaline. 

One fairer than my love? The all-seeing sun

Ne'er saw her match since first the world begun.

Then, a few hours later, he sees Juliet and is every bit as interested in her as he was in Rosaline.  It might be a bit crass, but I always get the feeling that Romeo is interested in Juliet because she is "the flavor of the week."  She is gorgeous and available, and she returns his advances with romantic words of her own.  Romeo is interested for all of these reasons.  

By the end of the play, I do think a real love has developed between the two of them.  The best evidence that I have to support this is the fact that both of them would rather not live at all than live without the other person.