OK - I don't have a great deal of knowledge about this, but didn't want to leave you unanswered. I'm sorry to hear your little boy is being bullied, that's very sad, and definitely something I would mention to the consultant.
I think you have to got to the consultant fully armed with information, so from now until his appointment I would keep a detailed diary of everything he eats, and any exercise he does, so you have the facts at your finger tips, that way they can't fob you off by saying he must be eating more than you think or something like that.
It doesn't sound as if he is eating a terrible diet, - it sounds like what most kids eat to me. How are his portion sizes, that might be one area you can cut down a little bit, - or increase the proportion of vegetables to carbs on his plate.
But it's very hard to make suggestions until you know what the consultant might say, there may be an underlying medical problem that is making him gain weight and that really needs to be sorted out first.
If all those things are ruled out, then I think you need to insist on seeing dietician, to talk about what things he can eat that will help him have a healthy weight while not making him feel hungry or as if he isn't allowed any kinds of treats - he's very young, so its important I think that he doesn't feel he's missing out. But dieticians usually have lots of suggestions about fun food which are also healthy.
I imagine with his hypermobility (which I know is a very painful condition) he finds exercise hard, are there any things he can do which aren't painful for him (I'm thinking perhaps swimming - but apologies if I am being ignorant and he cannot manage that)
Anyway - I wish you luck, go in armed with details and facts and insist on action from them, - don't let them hurry you or fob you off, it's your consultation and you are entitled to get the best from it.