I cried for a month at meetings.
Part of it was my brain's hyper-sensitivity in early sobriety and part of it was the psychological ramifications of the causes of my drinking and then what I've done while drinking.
You are not the only one who cries through meetings. It gets easier in time. The hyper-sensitivity diminishes. At least in AA it is a safe place to cry - people there get it. (Well, a lot of them do.) It's good to cry. Something is trying to come out, and until it does you cry.
I stopped going to meetings after 120 days. I haven't picked up a drink, though. There is a lot of wisdom in those rooms and if life seems baffling, there is help in the rooms too.