If the available sample is too small, some questions may not be answerable via statistical means, at least with any high degree of confidence.

This one may not be answerable via this methodology. Even if you did all 200 countries, there just may not be enough high quality data to reach a satisfactory conclusion.

I'm not even saying the conclusion is wrong, I am saying the data doesn't exist to determine if it is right OR wrong.

The question is how many variables have they tested before settling on obesity.

Every single signal points for non-significance of this article. What, of course, is just reason to test it in another population. But instead people will just keep repeating it as if the findings were true.

I think the limit is closer to 400 since some federal states have states as big as many countries, but very good point.