Romeo and Juliet are referred to as "star-crossed lovers," meaning ill-fated lovers (I.Prologue.5). Hence, it is very appropriate for Shakespeare to use celestial metaphors, such as star metaphors, to characterize both love and beauty. Shakespeare's characterizations of love and beauty serve to illustrate the conflicts of man vs. man and man vs. fate.  

The first star metaphor is spoken by Lord Capulet to Paris. When Capulet invites Paris to join the party tonight, he also invites him to not only survey Juliet, but to also survey other women at the ball, to make certain that he positively wants to choose Juliet for his bride. Capulet masks his invitation to survey other women by referring to women's beauty as starlight, as we see in the lines,

At my poor house look to behold this night
Earth-treading stars that make dark heaven light.
Such comfort as do lusty men feel... (I.ii.24-25)

The phrase "Earth-treading stars" is a metaphor for beautiful, dancing women. Hence, using this metaphor, Capulet is inviting Paris to survey all the beautiful women at the ball. In referring to beautiful women as stars, coupled with a reference to Paris's lusty emotions, Capulet is making an allusion to the theme of man vs. man. In this play, We see the conflict of man vs. man expressed in the theme of unrequited love. Paris is in love with Juliet, whom he can't have, therefore, his own emotions are battling with another human being's emotions, namely Juliet's. Similarly, at the end of the play Paris literally battles with Romeo, Juliet's true husband, which is another occurrence of the man vs. man conflict. Hence, we can see that a metaphor about stars coupled with a reference to lust can help portray the conflict of unrequited love, or man vs. man.

Another star metaphor, albeit an extended metaphor, can be seen when Romeo compares Juliet's eyes to stars, saying,

Two of the fairest stars in all the heaven,
Having some business, do entreat her eyes
To twinkle in their spheres till they return. (II.ii.15-16)

Since Romeo is saying that her eyes are "twinkling" like the brightest stars in heaven, he is metaphorically comparing her eyes to the beauty of the stars. Since Romeo and Juliet are also referred to as "star-crossed lovers" this analogy can also allude to their upcoming deaths. Hence, any metaphor about stars that are used to describe either Romeo or Juliet can be seen as illustrating the conflict of man vs. fate, because Romeo and Juliet are both fated to die.