When Balthasar, Romeo’s man enters, why does Romeo expect that he will have letters?
I assume that you are talking about the part in Act V, Scene 1.
In that scene, Romeo is in Mantua. Remember, he has been exiled there. He had to run away from Verona when he killed Tybalt in the street fight where Tybalt had killed Mercutio.
So now Balthasar has come from Verona. Naturally, Romeo thinks he might have letters. He expects that Friar Laurence will be trying to get in touch with him to let him know how things are going and whether it will be safe for him to come back to Verona. Remember that the Friar has said, back in Act III, Scene 3, that he would work on straightening things out with the various people in Verona.
Back in Act III, scene iii, the friar actually told Romeo he would send Romeo's man to deliver letters of news. This is in the last about 30 lines of the scene.
Romeo, naturally therefore, would believe that any word coming from his man (Baltazar) would be directly from the friar.
Likewise, when away, one hopes to hear from family and friends. Romeo was likely very lonely and thirsting for evidence from those who loved him that their love remained. But poor Romeo, this was not the case.