10 stone overweight means your eating is seriously disordered. That's not just "enjoying food a bit too much". I'd focus on getting help for that first. Your weight affects every area of your life.
It's bound to get you down and it's not nice for other people if you're quite negative a lot of the time. I'm not judging you for being negative by the way, I'd be bloody negative if I was carrying 10 stone around all the time. That's like carrying a whole person! Your life must be really hard, just doing daily tasks must be like climbing Everest.
People have busy lives and can be selfish. They want friendships that are easy and that don't require much thought, particularly in the early stages of getting to know each other. I imagine trying to include you would require a lot more thought than just inviting you along.
For most of the things I do with friends, you might not be able to manage (or I'd worry you wouldn't). We go to gigs that mean standing for hours - if you're carrying an extra 10 stone, can you do that? We go to the theatre, there are narrow aisle steps and the seats are tiny (even for me at 8.5 stone). I'd worry about you coming along and being embarrassed when you can't fit in the seat. We hired a karaoke booth for a friend's birthday but when we got there, there were multiple flights of stairs to climb. My legs were aching when we got to the top and I like to think I'm reasonably fit. We went to a restaurant and the tables were close together and the chairs weren't very sturdy - fine if you're slim, we all had a great time, but could be awful for someone overweight if the chair broke, or at least very uncomfortable sitting there with no space and waiters unable to get passed your chair. What I'm trying to say is that even the things that one would presume you could join in with like restaurants and karaoke can have barriers that mean you can't go.
Try to think of things you can do and places where you feel comfortable going and invite others along. And if someone invites you to something, only say yes if you're definitely going. Don't let people down or they'll stop inviting you.