We've just kind of done this with my 12.5yo. I've posted my story on another thread so will copy it here:-
I have a 12.5yo girl in S1 who is 60kg at approx. 5ft 1in, which is overweight. In stark contrast to your daughter, she doesn't seem to realise it and calls herself skinny like her brother and sister (who are both very skinny). She is quite slim & tall all over but has a large tummy (never complains about any pain).
DH and I are overweight (I'm morbidly obese which I am working on) and we are very worried about her, but trying to tread very carefully as we both clearly have our own food issues.
DD is quite greedy, she doesn't eat a wide variety of foods, but what she does eat is in big portions i.e. a whole pizza etc. She doesn't have a varied diet so eats the same sandwich day after day for example. She's also now in control of her diet to an extent as she started at high school in August so chooses her own lunches and some snacks.
She swims regularly with a non competitive swim club but doesn't do a lot else due to a recurring injury in her leg. She has sat out of PE for most of this term (necessary). We are going to start family walks though, if this rain will ever stop!
We have really realised her weight is rapidly rising this week so have decided to implement a family healthy eating strategy going forwards so change white bread to wholemeal, cut out the crisps, homemade pizza, wholemeal pasta, less treats/McDs. And maybe ask her to take packed lunch a couple of days a week. We will monitor how things are going, by eye - I don't want to regularly stand her on scales as she is so unaware of any issues, the only reason she was weighed in the first place was because she presented at A&E (something unrelated but they weighed her on admission).
I know this might not be helpful as we are dealing with different daughters, but its helped me to write this out and also to know I'm not alone. I can't decide if its better or worse that they realise - better because they might change their diet & exercise more but worse as of course you desperately don't want them to be unhappy.
I am very interested in similar stories and wish you all so much luck. I am terrified of my DD being overweight & unhappy but also don't want her know how worried I am or give her any food issues.
Our family chat and start to healthy eating has gone well, both older kids have accepted less treats & sweets and some small changes to what we buy. Its cod, new pots and green beans for tea, will see how that goes down!