This post and this post claim the seeming increase in 1980 isn't what it's made out to be - coming from cohort effects, the reversal of a slowdown in 1950 caused by wars/economic depression.
My sense is this is true, and obesity is best thought of as 'having increased since a bit after the industrial revolution', and the increase in 1980 just continues trends like 'food abundance increases, food is desgined to taste better' rather than being a step increase in rate. There is also probably a 'noise + increasing rate looks like a step' effect - if you take a smooth exponential and multiply it by smooth noise, it'll look like there are places when the rate sharply increases because the noise will temporarily line up with the overall trend of growth.
Note that there really isn't a single correct answer here - for reasons like https://slatestarcodex.com/2019/03/13/does-reality-drive-straight-lines-on-graphs-or-do-straight-lines-on-graphs-drive-reality/, which is why this is a bounty on interesting information as opposed to a yes/no market
100-200 bounty per good link / good relevant argument that I find interesting. 1k bounty if my position significantly changes (either towards 'more confident nothing particularly happened in 1980' or 'think its more plausible something happened in 1980'
the "bounty" is 5 because if I put in a 1k bounty that locks up the 1k forever, and this might just not get responses
Here is a study suggesting it accelerate due to a delayed consequence of sugar consumption:
https://www.sciencedirect.com/science/article/pii/S1570677X19301364
It further notes:
"The age-stratified obesity data we used run through 2013–14, and in the future it will be revealing to see whether teenage obesity has declined since 2014 as the sugar-driven model predicts."
I think that prediction is falsified (see table here):
https://jamanetwork.com/journals/jamapediatrics/article-abstract/2794534
I have never been satisfied with the sugar explanation myself, even without a kludged delay factor added in. I know this is a tiny part of a much bigger question that you're asking but thought I'd share in case of interest. If you're looking strictly for big picture conceptual arguments then feel free to ignore!