Romeo is obviously sad at the beginning of the play. His sadness there is due to his infatuation with Rosalind. This infatuation has produced in him many of the classic signs of Renaissance love-sickness, including melancholy, alienation, disorderly appearance, and unpredictable behavior. Many people in the sixteenth and seventeenth centuries would have argued that Romeo’s sadness reflects the selfish nature of his love, which is not true love at all. Instead of being genuinely in love with Rosalind as a soul, a person, another creature of God, he mainly desires her body. His desire for Rosalind is rooted in selfishness and is therefore not true love. It is, indeed, infatuation – a kind of foolish fixation on an external object, but a fixation ultimately rooted in self-love. The shallow nature of his “love” for Rosalind helps explain not only his initial sadness but also the ease with which he can easily abandon his fixation on Rosalind for a new fixation, this time on Juliet.
You do not specify which part of the play you are talking about.
There are many places where Romeo is sad. I'll talk about two of them.
Romeo is sad at the start of the play. He is sad at this point because he is in "love" with Rosaline. The problem is that she does not love him in return and so he is going around moping because of this.
Much later in the play, he is sad (beyond sad, really) because he believes that Juliet is dead. He is so devastated by this that he kills himself.
So those are two places in the play where he is sad.
In Romeo and Juliet , Romeo is sad not because of Juliet ( they haven't even met yet ) but because of a girl named Rosaline . Apparently no matter what Romeo does ( such as giving gifts , money ) Rosaline wouldn't accept his love because she has sworn to become a nun .