To clarify, there are two related but separate questions about obesity that are worth distinguishing,
What explains why people are more obese than 50 years ago? And what can we do about it?
What explains why some people are more obese than others, at a given point of time? And what can we do about it?
In my argument, I was primarily saying that CICO was important for explaining (1). For instance, I do not think that the concept of metabolic privilege can explain much of (1), since 50 years is far too little of time for our metabolisms to evolve in such a rapid and widespread manner. So, from that perspective, I really do think that overconsumption and/or lack of exercise are the important and relevant mechanisms driving our current crisis. And further, I think that our overconsumption is probably related to processed food.
I did not say much about (2), but I can say a little about my thoughts now. I agree that people vary in how "fast" their metabolisms expend calories. The most obvious variation is, as you mentioned, the difference between the youthful metabolism and the metabolism found in older people.
However...
Then you have the opposite type of people, whose metabolism stubbornly refuses to release the fat from fat cells, no matter how much they starve or how much they try to exercise... (In extreme cases, if they try to starve, they will just get weak and maybe fall in coma, but they still won't lose a single kilogram.)
I don't think these people are common, at least in a literal sense. Obesity is very uncommon in pre-industrialized cultures, and in hunter-gatherer settings. I think this is very strong evidence that it is feasible for the vast majority of people to be non-obese under the right environmental circumstances (though feasible does not mean easy, or that it can be done voluntarily in our current world). I also don't find personal anecdotes from people about the intractability of losing weight compelling, given this strong evidence.
Furthermore, in addition to the role of metabolism, I would also point to the role of cognitive factors like delayed gratification in explaining obesity. You can say that this is me just being "smug" or "blaming fat people for their own problems" but this would be an overly moral interpretation of what I view as simply an honest causal explanation. A utilitarian might say that we should only blame people for things that they have voluntary control over. So in light of the fact that cognitive abilities are largely outside of our control, I would never blame an obese person for their own condition.
Instead of being moralistic, I am trying to be honest. And being honest about the cause of a phenomenon allows us to invent better solutions than the ones that exist. Indeed, if weight loss is a simple matter of overconsumption, and we also admit that people often suffer from problems of delayed gratification, then I think this naturally leads us to propose medical interventions like bariatric surgery or weight loss medication—both of which have a much higher chance of working than solutions rooted in a misunderstanding of the real issue.