It would be a good idea to pedal the moped like a bicycle and engage it rather than starting it on the center stand. I'm heavy as well, so I do that instead. Personally, I think it's just easier to start as you are moving anyway.
To straighten out your kickstand, I'd recommend that you take the kickstand off, place plywood on a concrete floor or blacktop- put the kickstand on that. Then get a nice thick piece of wood, say, 4x8 or something like that and put it on top of the kickstand and use a sledgehammer and pound it back into shape. The wood will protect from dents and dings.
Another alternative is to use brute strength. I personally prefer to go that avenue- more control that way. You could put a rag around your kickstand, and place it in a good vise and put it in there good & taut. Get a pipe and place the other side of the kickstand in the pipe and use the pipe for leverage and bend it in the direction that it needs to be moved back to. That should work.
But, most metals, once they are bent, they are weakened for good. You might be better off buying a new kickstand and not pedalling on it.