I think the rub is actually here:

"The participants received either ultra-processed or minimally processed foods for two weeks before swapping diet for the next fortnight. Participants in both diets had access to the same amount of calories and nutrients like sugars, fibre and fat. People were free to eat as much or as little as they wanted. The results were striking. People on the ultra-processed diet ate about 500 more calories per day than those on the unprocessed one"

My understanding is that caloric intake is king.

Weight loss/gain is specifically tied to calories consumed vs calories burned, yes.

But that is not the purpose of the study.

2 groups of people, 2 diets, and the 1 group given an unlimited amount of relatively healthier food, chose to eat less of it and lost weight. The other ate more junk food and gained weight.

That implies that there are non-conscious factors at play and that diets may be more naturally successful if they are comprised of healthier less-processed food even without restriction.

Additionally, this implies that there must be an X factor that takes place in the processing of foods that causes overweight people to keep eating when they have met their caloric requirements.

For context, look at the data regarding nutrient density in vegetables over the last 60 years and see that the nutrients aside from fat/carbs/protein have been on a steady decline year over year.

https://pmc.ncbi.nlm.nih.gov/articles/PMC10969708/

When I put these things into perspective, my hypothesis is this:

Being overweight, commonly viewed as a weakness of character or a sickness of the mind or body, is more likely a symptom of some larger issue.

Evidence of this can be found piecemeal from studies on human diets the world over.

The foods that are readily available to people are making them sick, my guess is that this is from some form of malnutrition. This may be a nutrient malnutrition or some compounding effect that the overprocessing of foods has on the human body that isn't trivial to differentiate from its non-processed counterparts.

I feel it is reasonable to assume that in general overweight and obese people on an ultra-processed diet are overeating in a non-conscious attempt to compensate for a lack of fundamental nutrition in the foods that are available to them.

Therefore, to test the hypothesis, the underlying nutritional issues should first be addressed by eliminating ultra-processed foods from the diet and replacing them with minimally processed foods, the higher in "quality" the better.

Theory: An overweight person will naturally reduce their caloric intake when their diet meets or exceeds their nutritional requirements.

The results, listed in the article above, seem to suggest that this theory is correct.