typically the mechanism by which thyroid hormones are understood to affect weight gain is through appetite (calories in) and metabolic level (calories out) so they probably aren't really an exception to the calories-in-calories-out model
i mean as far as we know they don't enable you to digest carboxymethylcellulose or anything like that (one of the many common additives on my suspect list)
it's not totally inconceivable; some commensal enteric bacteria can digest carboxymethylcellulose, and they generate heat when they do so, and at least when it's cold outside that's heat you don't have to generate by shivering or physical activity, and we have such a poor understanding of what affects the intestinal microbiome that it's actually possible that thyroid hormone levels are important, but there's no evidence suggesting that this is the case as far as i know
but even on industrially produced diets most people probably don't eat enough carboxymethylcellulose and xanthan gum and shit like that for their digestibility to make a significant difference in their caloric intake; as i understand it the reason industrial food engineers use gums like these is that very small amounts of them can greatly increase the viscosity or gelling ability of foods, so you don't have to spend as much money as you would with more traditional thickeners like gelatinized starch
like, three grams of this carboxymethylcellulose i have here can turn 100 grams of water into a thick slime, but i would need about 30 grams of cornstarch to do this (which i would then have to cook)
(i think this is typical but your results may vary depending on the degree of functionalization of your cmc)
so if newly popular gums like this do cause obesity, it's probably through some kind of inflammatory mechanism or something, not by directly supplying calories
