Does your daughter have another parent or trusted adult in her life? You are completely the wrong person to be helping her through this, you’re absolutely awful and you’re going to destroy her confidence with ‘obesity is too accepted in society’ attitude - should we ostracise fat people then? Bully them? Deport them? Burn them at the stake?
OP, even if there is an underlying cause, it is very likely you are going to be the mother of a fat person for some time, possibly for life (losing weight isn’t a maths problem, 95% of people who lose weight without medical intervention like drugs or surgery will regain the weight within 2 years, over and over and over again). You need to get really comfortable with the idea your daughter is overweight REALLY quickly, because if you don’t you’re going to ruin your ‘open and friendly’ relationship with her really, really fast.
My suggestion is you stop seeing weight gain as a moral failing and reassess your very clear distaste for large bodies. Yes there’s health implications for some fat people, but it is very possible to reside in a larger body and lead a completely successful, normal life. Unless you think your daughters only worth in life will be how she looks?
Also, teenagers have sex and need birth control (especially fat ones with judgemental mothers, they crave the validation), if you don’t want your girl to be ‘that kind of girl’ I suggest you stop judging and start supporting her.
My mum was just like you most of my teenage years, I had sooooo many secrets from her as a result. Your attitude won’t make her thinner, it will make her sneakier and less likely to engage with any help you try to provide, however well meant. It turned out I had PCOS that went undiagnosed until I was 23 because mum thought my weight was my fault. In reality, I hit puberty and my hormones went absolutely haywire but because she had the same attitude to fat people that you do, it was completely missed until it was far too late. I now have my PCOS mostly under control, but it meant 10 years of fertility problems for me which could have been minimised had I been diagnosed and treated as a teen.
You will lose her, OP if you prioritise your piety over fat people above her well-being.