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.
Also, the physical effort involved in being in the workforce in the developed world can be almost nil. A lot of people have to stand up all day, or pick up boxes, but that's far from subsistence farming or hand-washing clothes.
Or even: in developed countries, most work is not physical labor.
Human culture and gender differences is overwhelmingly complex subject. This research is trying to establish direct relationship between estrogen and obesity, but hormones might have subtle but signficiant effects on human culture.