That's is part of it, but not the single answer. Since cheap sugar has been around for a century at least. Epigenetics, lack of exercise, cultural changes, car dependence, also factor in.
More to it than sugar. Processing subtracts as well as adds. Pthylates, endocrine disruptors, lots of good stuff in our water and food now. Gut biomes aren't the same either, thank you antibiotics.
(Plus/minus on antibiotics is plus, I'll take alive and obese over painful and dead most days.)
Not talking about fortification. Food processing in this context means taking food through some incredible steps in order to create a cheap, "addictive" product you can sell. This often involves adding some kind of sugar.
We agree on that. It subtracts and it adds other stuff too. Mac and cheese add pthalates in the cheese from the rubber used in the machinery. It could be as simple as the sugar, but have you controlled for any other variables as well?