The only evidence that I currently have available is the Netherlands. The only western country to have a reducing obesity index, by 2030, predicted to be 8.5% down from 10%. Their diet is a very typical western diet.
However their transport system and their urban planning is hugely focused on prioritising walking and cycling with good provision of local amenities within easy cycling distances. Yes, you build higher density urban environments, but this is a good thing.
In fact if one wants to loose like 10 kilos quickly, just climb to Everest. Most of that weight will be spent on body heating, not muscular work.
That also explains why butter does not harm people in Tibet. It is not stored as body fat and goes directly into body heat.
And anecdotaly I have a co-worker who was into serious climbing. Before a high climb like over 6km he on purpose typically gained like 5 kilos of weight and still came back learner from the trip. And he knows for sure that that was due to coldness as on much more physically demanding trips at warmer altitudes weight loss was much smaller.
This has been given as one of the problems that Scott faced when man-hauling sledges on the Antarctic plateau at 3000m.
http://www.livestrong.com/article/317620-how-many-calories-a...
"even mild cold that doesn't cause you to shiver starts to burn through those brown fat stores, jumpstarting your caloric burn rate."
Famously, Inuit team drivers for Arctic expeditions would eat all the butter out of the food supplies first.
The Dutch are unusually active in general, and this may well be down to their environment encouraging being active from birth.
I'm not saying diet is not a factor (1 in 10 are obese), but, the UK is currently at 27% (1 in 4), the worst in Europe heading for 35% (1 in 3) obese by 2030 with a similar diet profile to the Dutch, indicating about 25% of obesity will be down to environment. The US is even worse. Both the US and UK have an extremely car dependent design philosophy. One that the US is rapidly tackling through road diets. However planning is still a step behind at the moment.
I'm not disputing diet is vital, but if you have to get into a car to do a 0-5 mile journey because the "roads are too dangerous to cycle" or you won't let your kids walk/cycle to school 2 miles away you end up with an obesity problem no matter how good the population's diet.
You are right in one point: If the only thing you eat is butter with your veggies then you do not have much of a problem in terms of a cardiovascular epidemic.