I don't particularly buy it. Again, sure, maybe it has a statistically significant effect, but it is undoubtedly dwarfed by people chugging sugary drinks and being more sedentary. A casual search suggests sugar consumption has increased 9 fold since the 1800s and 2 fold since the 1900s. The poor in particular are cornered into purchasing sugary foods due to weird economics around corn subsidies. And what do you know? They're the fattest by far.
If it were mostly environmental you'd see broader gains. variation. But in my little bubble in upper middle class Massachusetts, I don't know ANYONE who is obese. In other areas of the country it's hard to find anyone who isn't.