I'm conflicted because I was appalled by the headline, but then reading the context, I could see your point of view. She needed support and encouragement, not horrible words. But you'd tried that. She obviously wasn't happy being that overweight, or she wouldn't have tried to hide it from you initially. You had the same goals - you both wanted her to lose weight and you were willing to support her and do it with her.
My husband and I went on a diet together - not to lose weight, but to try and tackle a health issue. We did it together. He didn't complain. It accidentally cured his asthma. It didn't cure my problem that it was designed to treat. We've since shrunk his cancer on a raw vegan diet, so it's no longer visible on a scan. We do these things together to achieve shared goals. He now has Parkinson's - another blow. I am going to all his Parkinson's meetings and appointments and plan to take part in the Parkinson's exercise programs. He is not on his own. We are a team.
To me, this is like what you were trying to do with her - achieve mutual goals together. I guess the thing that perhaps was missing, was trying to get to the bottom of why she'd not stick to the plan. I imagine she needed counselling too.
Sorry it didn't work out and you regretted it in the end. It sounds like she was lovely. But honestly, I think it takes two to work at things, and it would have been better for her to find the motivation to be more healthy.
People can and do change when they want to.