Thank you everyone. She doesn't really get enough exercise, but neither is she a couch potato. Easier said than done to get time walking with her alone, but V good idea - will try to fit it in.
She raids the fridge for leftovers and pieces of ham, bread, cheese. There are no biscuits or cakes or crisps in the house, and she's good at not helping herself to those if we do have them in. But if one of her siblings or she bakes a cake, she'll nibble it all day unless I get it out of her reach.
The thing is her siblings are all v slim, so I kind of want to get them eating seconds if they want it and it makes an issue out of it if I say yes to them but no to her.
She has some self-esteem issues, and I know it's normal for nine-year old girls to struggle with the transition from little girl to pre-teen...and she's having to manage the beginnings of puberty as well much younger than she would normally.
When she's going through a bad adolescent-style patch and acting up, we notice she eats more then. It's like she doesn't like her behaviour, and translates that to not liking herself, and then her looks, and then gets in a cycle of punishing herself by behaving worse and eating more. I don't understand how to help her break out of it, but I'm doing my best - reading, talking, and also talking to her and listening to her.
But even if the root of the overeating can ultimately be fixed, in the meantime she's getting bigger and bigger :( I think taking control of the kitchen is the right idea. And also drinking more water.
I'll try and do some just dance with her every day - in the absence of being able to get out and walk daily because of the other kids, it'll be a start and something she can do with me.
And I'll take her for long walks or bike rides when her dad's around. Thank you - felt a bit adrift back then, but feel like I have a bit of a plan now.