Mine has teared up sometimes. I have some sad stories, and he's a bit of a sap. To me it's very natural that he would cry, and his orientation is very much about being genuine and connecting on a compassionate level. I think some therapists who work differently would be less free displaying their feelings.

If it bothers you it might help to talk about it. I think people's responses to therapists' tears tend to vary a lot, so it's not unusual to feel uncomfortable with it.