The amount of times I have seen parents post photos of their kids and say that he's or she is not over weight, but people have clearly lost the perspective of what is over weight. I can't see how she isn't if she scored obsese, if you has Sian overweight then she could have been barely boarerline but to be obsese then she has to be carrying extra weight.
Children are meant to be lean, you should be able to clearly SEE their ribs!
The good news is, you are now aware of this, which is why it's done and she is still so young so there is so much you can do to help her, I would suggest finding something other than food to reward good behaviour, just because for anyone an association with food and reward isn't healthy.
You totally have this though, there is no reason to be upset, no one is condeming you at all of your Daughter, but its a good opportunity to start looking at what healthy eating is, I say that because it means different things to different People, so read up and what you believe and what you want your futures to be like. So for example we eat quite clean, we go indulge from time to time, but I have found that things I consider good or bad and Are different for others. For me, nothing is really forbidden, but we avoid anything artificial, I would choose butter over margarine for example which would be considered unhealthy, some clean eaters avoid all diary and meat where as I just eat moderately.
Anyway, I just say that as it's about changing how you eat, not going on a diet. Your daughter doesn't need a diet, but just help her limit sugars and things will change, it's not something to be upset about, most people at some point decide they need to change what/how/when they eat.
Chin up, there is nothing go be upset over, her body will continue to change, so just moderating her diet will help.
Kids are all different shapes and sizes, it's hard to really tell, which is why the BMI is used, I have 4 kids, and they are all different shapes and sizes, I have twins in the mix who have completely different body shapes, one looks much chubbier because he is much much shorter than his twin, the taller twin looks skinny, weight wise the skinner twins weights significantly more, both normal weights but the taller one is much further up the bmi scale than the shorter one, so it's really hard to tell. Also kids eat and like different things, on the whole they eat really well and no major issues but the lighter twins would rather have dessert or fruit than proper food, he likes junk foods, like chips, pizza, etc which the others are less fussed about, so I do get it, it's hard, but it's possible. I totally feel genetics has a major role as well. My husbands family are all slim, sometimes even underweight, but it's not from lack of eating, they eat really well but are just slim, my family and me put on weight even thinking about food lol... but worry less about the weight, worry more about having a positive relationship with food and exercise, move your treats to a one night thing, 2 at most, so that she isn't denied but she learns moderation.
It's so difficult writing, because I don't what to come across patronising, I do understand why you're upset, don't let it get you down, turn it into a positive. Hope you're ok x