I don't think your weight is an issue. I think what could be good is for you to take a step back. Find a better riding school or look for a steady plod maybe on part loan.
Just because you can stay on the horse when it's cantering doesn't mean you necessarily should do it. it sounds like you need some support and to start from the ground up and they are not giving this to you.
Riding schools in my opinion rarely do. A lot of people don't because a lot of people don't understand what it's like to lack confidence.
You don't build confidence with speed and difficult stuff. you build confidence by just being around them without anything stressful.
If you lived near me and I had a suitable horse I'd get you handling it on the ground. You lack confidence because you are worrying about how the horse is going to react because he could react and hurt you.
So I'd have you touch the horse and gradually put more pressure on different areas of the horses body so you could see for yourself what's going to happen if you do this. I'd get you leading him places so you can see what he's going to do.
There are always going to be the odd ones you don't see coming but if you spend enough time gradually exposing yourself to more and more you wouldn't have this huge crash when you do get that odd incident pop up (and yours are some pretty unfortunate and scary ones!).
Really don't pay money to be frightened. Find somewhere (trekking centre idea was good) you can just spend time relaxing without pressure.
I broke several bones (two complete breaks in my right upper arm) falling off once. my mum bought me my own so I had that advantage but I couldn't tack him up or anything because my arm took sooo long to heal and one day I just started walking him to the wall near the menage. I'd walk around to a slope that went up to to wall and then just walk around on him bareback. I couldn't do anything else for ages but once I could I don't remember being scared.
I did have a meltdown about a week after the initial accident though where I insisted he was out to kill me just because he came over to sniff my jacket pocket though. Confidence issues are the worst xx