Blaming it on food scarcity isn't the whole story. It's not enough that food scarcity stopped. It wasn't carbs either, as there are cultures without carb scarcity that weren't obese(Though we do put corn syrup in everything now).
My guess is that it's a dopamine addiction. We understand that sometimes we must do things we don't like, but the idea of eatings things we don't enjoy scares many people.
It's also how corps package food, and the ones that make their foods the most addicting(the most dopamine -> the most pleasure) survive.
Some kings in the past had massive obesity problems, like Henry VIII. Apparently for him it was forced immobility following a hunting accident. Most people in the UK just haven't been able to afford to get obese until the last several decades, and I warrant companies have learnt how to hook us on high-fat and high-sugar foods to make bigger profits.
https://en.wikipedia.org/wiki/Obesity_in_the_Pacific
If you follow the "see also" from that article studies find the genetic factors towards becoming obese in a favorable environment to be different in different ethnic groups, from 6-85%.
So a theory that fits the statistics is that colonialism brought in a favorable diet for weight gain to everywhere(?) but the percentage of people who became obese when subjected to a favorable diet was largely a factor of local genetics, genes most useful in an unfavorable environment did well and put the peoples in those places at the top of the list for obesity rates.