Just eyeballing a map, the countries that pop out as both having Starbucks and not having an obesity problem are China and India. Other than that, it looks like most of the countries that have Starbucks have obesity rates over, like, 20%, which seems pretty bad.
This isn’t to say Starbucks is causing obesity, of course. Most likely they are showing up together as the economy develops.
I do think it is worth noting that obesity is a pretty widespread problem, not uniquely American or anything like that.