Society is getting bigger, but it’s not getting bigger uniformly. There are variations based on geography, occupation, race, income, religion, shoe size, you name it. Let’s start with the US.
The relative amounts seem to be similar. That is, the biggest states in 1994 are still the biggest ones (roughly), but they’re bigger now.
The relationship between wealth and obesity is complicated. In rich countries, there is evidence that being poor is a risk factor. Figure 3 from the review above shows that obesity was 26.7%/29.4%/23.6% for low/med/high SES men (not a typo, medium has the highest) and 37.8%/34.5%/29.9% for women (year 2000). Many articles just say something to the effect of “poor people are fatter” without much thought. There is certainly literature supporting that notion . The basic mechanism is that calorie dense food is cheaper per calorie, and people tend to eat more calories overall when their food is more calorie dense . This is not true in all countries.
Depending on how you slice the data, it can look a bit different. Everybody uses NHANES data, and most studies divide people into income quintiles. One paper just divided people into “poor” and “not poor”  and found that while the prevalence of obesity among the two groups was the same, the poor had higher average BMI. Meaning that a poor obese person was generally much fatter than a rich obese person.
Along the same lines, the real fast-food restaurant price, the real food at home price and the real full- service restaurant price have negative and significant effects [on BMI] at weighted sample means.
Coming next week (probably): A comparison of different countries as they stand today. Working title: Why is Japan so thin and the US so fat?