He is almost annoyed by her. In fact, I believe Camus puts this in here for the purpose of contrast. As Mersault falls asleep at the vigil and we readers can almost feel his complaint about having to be at the vigil, this woman demonstrates how Mersault should be feeling. She weeps and he does nothing. Even if Mersault and his mother had a terrible relationship, an appropriate human response during this situation would be to at least try to console the woman. He could attempt to sympathize with her, but he is rather apathetic and listless toward her. He doesn't care about how she is feeling.
This is going to be an important attribute of Mersault's character to hang onto for later, so keep it in mind.