It's actually not as uncommon as one would think for a man to feel attracted to a young teenage girl. Girls develop much faster than boys, and at the age of 13, or even 12 or 11, girls can look deceptively like young grown women. We can assume that Juliet may have been a fast developer as not only did Romeo fall in love with her, but Count Paris was in love with her long before Romeo even ever saw her. We know that Paris has been in love with Juliet for quite some time as in the very second scene we see him asking Lord Capulet for Juliet's hand in marriage, not for the first time, but for the second time, which we can gather from Capulet's response to Paris's question, "What say you to my suit?":
But saying o'er what I have said before:
My child is yet a stranger in the world
Let two more summers wither in their pride
Ere we may think her ripe to be a bride. (I.ii.6-11)
Since the phrase "but saying o'er what I have said before" means that Capulet is repeating himself, we know that Paris has asked for Juliet's hand before and has received the same answer before. Therefore, we know that Paris was in love with Juliet well before Romeo ever saw her and that she must, therefore, be a very fast developer.
However, while marrying at a young age certainly did happen, it may not have actually been as common an occurrence as the play or other works of literature indicate. While Romeo and Juliet was written during the Elizabethan period, the play actually reflects historic events that took place during the Renaissance. During this time period, it was certainly legal for girls to marry at the age of 12 and boys at the age of 14. Many girls did marry close to this age because the life expectancy rate was much lower than it is today ("But Was It Love?"). However, studies through the analysis of marriage records have shown that, especially for the noble class, the average marrying age was in the mid-twenties. Upon average, women married around the age of 23 while men married around the age of 26 ("The age of marriage").
Therefore, while Shakespeare's play depicts a common occurrence, it does not depict the average occurrence. While it is not unlikely for a man to fall in love with a teenage girl, it certainly isn't the average occurrence. For today's audience, the young ages of the couple add to the drama and tragedy of the play; it's very likely, due to the average marrying age, that an Elizabethan audience would have responded in the same way.
Romeo and Juliet is not a conventional love story, but merely a hyperbolic portrayal of two young lovers. If you consider the maturity difference between men and women, along with the fact that 13 was an acceptable marrying age in the late middle ages, it can be assumed that this situation was completely normal.