Its not weird, I have been having the same problem. I have heard how some people go and just cry their eyes out the whole time and I have not but had a tear or two run down my cheek. I was thinking that something was wrong with me. It made me feel that maybe my counselor was getting frustrated with me but that is not the case.
They see so many different individuals and for different reasons we all process things in different ways. They expect that. I started to shed a couple tears the other day in my counselors office because she aksed me just to relax, I am often tense in there, when I relaxed it was a little easier but when a couple tears fell, I just stopped, I have not been able to let it all out, not that I don't want to. As I shed a few tears , she said you were really never able to do this with people were you, I said no, that I never do. Its always when I am alone in my room. I told her I felt stupid starting to cry infront of her, she assured me that I was not stupid:)
I told her that I know I am difficult and sometimes as feel like I am being a brat because I have not been totally open at this point. They expect this, its not new to them, so whatever you do, don't be afraid. Its all a part of learning to trust and it can take time.
I verbalized to my counselor the other day that it is not her personally, but its me. She said she knows its not her that she realizes I am probably still not feeling totally secure with her at this point and thats fine. Thats what they are there to work on too.
Just hang in there, if you feel you want to take that risk even if its just a tear or two don't be afraid.