Just reading the OP made me feel stressed. You are putting so much pressure on and there is no doubt at all that the pressure will make any issues that are causing the weight gain worse.
I am really shocked that you have already raised her weight as a problem. It is hard to explain why but that just makes the guilt and dysfunction around food so much worse when you are overweight.
She is still young enough for everything to change, but if she becomes obsessed with her weight and diets now she could be locked into a binge and diet cycle for decades, for life perhaps. Being overweight now does not mean she will have problems in the future. Being pressured now and having more anxiety about food does.
It is a bit late to undo the damage but back off on the weight. Do not mention it, never ever guilt her about food. Focus on improving her mental state generally and taking food and weight out of it. If this is self harming then making weight gain and overeating this taboo thing will only make that worse. Neutralise them a bit. Self hatred and shame never made anyone take better care of their bodies.
Make sure healthy eating is modelled for her and options available, but put no pressure on about it. Say nothing about appearance and clothes except for compliments. It may go against the grain to act as if her being fat is ok with you, but believe me stigmatising it will make the cycle worse. If she is ever going to be slimmer then feeling confident and happy is the starting point for that.
Do not make exercise about weight loss. Promote it as something to enjoy but not as a weight loss tool, it is mostly diet anyway. You'd have to exercise for hours and hours every day to offset even the tiniest increase in food.