My field of study and my experience is not in medicine or public health, but GDP vs. obesity rates seems like poor evidence for this particular hypothesis. For example, one hypothesis I can think about that explains this is that in developing countries, it could be possible that women are often homemakers, and therefore, they don't have as much physical exercise as their male peers. In developed countries, where women are more free to work, the obesity rates are comparable...

I mean, I don't see a slam dunk "See, it's female hormones!" There could be a number of things from culture to lifestyle choices to work-life balance that can have affect on obesity that might correlate with GDP. They should have at least controlled against that, and I see no evidence of it.

The correlation itself is interesting, even without the female hormones.