Here's some more anecdotal "diet of nations" theories:

Climates with less sunlight and more cold require humans to consume more meat to absorb its Vitamin D. Nations that aren't as far north don't have to eat as much meat, or they may be closer to a coast and consume more fish/shellfish. In addition, the warmer climate may lead to its inhabitants being outdoors more often, which may lead to more overall exercise.

A food culture based on centuries of the local inhabitants using what they have available may lead to increased health. For example, if the local food happens to store well and can be harvested en masse, and isn't threatened significantly by drought or floods, they may just naturally eat less food because it's availability is greater than those of other cultures. For example, Freekeh is a mediterranean grain staple which is harvested early in the season, which reduces the threat of rain, drought, pests and vermin, which not only increases the total average yield but reduces the need for chemicals to ensure a good harvest.

Another factor which may affect the diet is the length at which one needs to go to harvest their food. Some foods are quite labor intensive to gather or prepare and thus a lot of time and energy will be taken just to get the food ready to consume, while other foods can be picked off the ground and eaten. Some also can only be harvested at precise intervals while other are available nearly year-round. This may lend to either a "storing fat for the winter" gorging when food is available, or the opposite, eating lightly and occasionally whenever it is desired.

Finally, there are general cultural differences when it comes to how and when to consume food. In Mexico (and I would assume many parts of latin america) it is typical to have a small breakfast, a quite large late lunch and eat dinner after 9PM. In other parts of the world the custom may be to eat a pastry for breakfast, a light lunch and a healthy balanced dinner early in the evening with different beverages throughout the day to tie one over.

When it comes to America, there seems to be a culture of sport that many parts of the country are lacking. If you see some kids playing soccer, chances are they're mostly not "white americans". Baseball used to be a favorite summer pasttime, but I don't see that many kids playing stickball in the streets these days. And in winter, besides ice hockey in the north you won't see a whole lot of outdoor sport played by kids or adults in America (unless it's some sort of amateur league team sport). Many other countries play sports year-round which no doubt contributes to a healthier overall lifestyle.

Finally there's our unique food culture and history. We're not a very old nation, so there hasn't been a very long time to develop a history of eating particular food. On top of that we're a geographically large nation with lots of different food staples throughout different regions. And as modern progress has sped the production of new ways to make and consume food, our culture has embraced the cheap-and-easy mode of bulk consumption that encourages we pay an additional $0.50 for another 10 ounces of soda. It's just too damn easy to eat unhealthy crap in our country, and we're almost proud of that. Compare that to nations that have eaten the same way for centuries and don't have the same history of new food businesses pioneering ways to produce crappy food, and you can see how our way of eating is more of a popular novelty than a real food culture.

I'll leave the food influences by religion of a region to someone more familiar with that, but it's safe to say that religion has influenced diet for thousands of years.