I've been supermorbidly obese.
As she is a child, she doesn't have money of her own to buy food. This means that if it isn't in the house, she can't eat it.
Trying to go straight to weightloss when she is actively gaining would be extremely difficult. I'd suggest that you look at maintaining as a first goal and then gradually adjusting what is available to just creep in under what she burns in a day. Weighing is not beneficial, especially if she doesn't want to do it.
She's using food - probably high carb, high sugar, high fat, easy to eat with the hands - to give her a calm high and to squash down unpleasant feelings, such as being tired or sad or anxious or angry or everything, really.
At that weight, it's certainly not starvation rations to begin maintaining and then losing. Which is actually a good thing, as it's less unpleasant when you feel that you're still eating well.
The binge trigger foods tend to be the ones you know aren't particularly nutritious - biscuits, cakes, chocolate, sweets, ice cream, desserts, sweet or savoury pastries - and easy grab and go things like sweetened cereal, bread, crisps (for the behaviour of taking and eating six packets in a row, not the actual crisps themselves), that kind of thing. And drinks - milkshakes, fizzy drinks, squashes/cordials. If they're not in the house, she can't have them.
However, the impact of not having them can be upsetting. So there would need to be some alternatives - she might not like them as much, but if she is genuinely hungry, she'll eat them (subject to the usual MN thing of excluding ARFID, Autism, etc, etc) - maybe in larger quantities than you'd prefer but probably fewer calories and greater nutritional value than a box of cereal and two triple packs of sausage rolls, for example. Things like six hard boiled eggs, cooked prawns, mini mozzarella balls, individual cheese packs, pitted olives, homemade potato salad with a small amount of mayonnaise, chopped spring onions, tomatoes and cucumber, artichokes in lemon and olive oil, cooked chicken in olive oil and herbs, cherry tomatoes, capers, that kind of thing, plus some 'I need something to be eating' things like celery or carrot sticks, as it's bloody difficult to overeat carrot sticks when you just want something to be physically chewing on. The other thing with this is that it slows her down - is she actually hungry, does she want to take the time to put some mozzarella on a plate with cherry tomatoes, olives and some other bits, or did she just have a craving for carbs again and can't be bothered with the effort? It's higher protein and greater nutritional value to the foods.
Then you provide full meals. You cook enough for a large portion - handfuls, not saucepan-fulls, to maintain or lose weight at 17 stone, she can eat well - potatoes, pasta (perhaps the gluten free varieties will help, as they tend to include higher protein sources such as lentils or chickpeas in them?), steamed rice without oils (and suchlike from packets) with lots of vegetables, meat, fish, seasonings, herbs, spices, lots of flavour. Rather than a high sugar pasta sauce, you can make one that tastes good and naturally sweet by taking 5 minutes to sweat onions, adding tomato puree and tinned tomatoes. Or by cooking cherry tomatoes. Instead of a cheese sauce to smother pasta so it slips down easily, you can use full fat cream cheese and melt it in the cooked pasta, adding frozen petits pois and small amounts of cooked bacon, topping with some grated Parmesan. Or do cauliflower cheese with white sauce and strong cheese instead - similar taste but you're getting the sauce without pasta calories.
Buying good bread but not huge quantities means she isn't completely cutting it out - instead of a loaf of white sliced a day, something that needs to be cut, can be in larger pieces, can be eaten with peanut butter or olive oil with balsamic, that tastes of something and has some structure will be more satisfying. If she'll eat them, avocadoes are great - avocado toast with bacon may have the same calories as a bowl of cereal or porridge, but will keep her feeling fuller without a sugar crash an hour later. Rather than having a cake or flapjack, full fat yoghurt and fruit will also give sweetness and nutrition.
Increasing the nutritional and satiety value of her food will help. If she's not going out, she's likely to be low on vitamin D for a start - supplementation could help - the fizzy vitamins (Berocca or Redoxon taste very much like a fizzy drink - other brands taste like crap) can help here.
If she starts feeling healthier, this might encourage her to move more. Rather than crappy school PE, there are thousands of things that feel good - strength training, yoga/pilates/ballet barre, aquafit or swimming with a leg suit rather than a standard costume. She's not going to want to be thundering around to an exercise video. It'll hurt. What could help there is supportive leggings - there are cheap ones on Amazon that do the job better than crusty cotton ones that rub and blister. Decent running shoes with orthotics will help support her ankles and encourage her to use her leg and core muscles. A good sports bra will be more comfortable and doesn't have to be limited to exercise. Any movement beyond walking to the fridge and back is a result.
And sleep. She needs sleep - decent bed, decent bedding, fresh air and darkness to get the best out of it.
She might decide that she actually starts feeling better and wants to lose weight/be healthier - that would be wonderful.
She may not be the slimmest person, she may choose as an adult with her own income to go back to eating foods that increase her weight - but if a rejig of what you provide and support her with (and it's perfectly possible to lose weight on 2000+ calories a day without really feeling it if you're large, just so long as you're just a few hundred under what it takes to move yourself around) can give her a hint of a healthier and happier feeling, it won't hurt to try.
Finally, I would say one thing about money. Bluntly, if you're buying enough snacks and foods to facilitate a child reaching 17 stone, you've got enough money to fund healthier foods and activities.