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Study links long-term artificial sweetener intake to increased body fat adipose tissue volume
(www.sciencedaily.com)
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But satiety is very complex, and it's possible that sweetener replacements make people hungrier in the long run, leading to weight gain.
IIRC that was a popular opinion about artificial sweeteners for a while because pigs are raised on food with sweeteners, to make them eat more. That doesn't mean sweeteners make you hungrier though, just that pigs like to eat sweet things so they eat more of it.
It's been a while but my most recent information was that this correlation couldn't be confirmed. Sorry, can't provide sources, just what I remember from a while back, so feel free to take this with a grain of salt.
TIL I'm a pig
Today we unite, my pig sibling!
Supposedly the study already accounted for that (amount and quality of food eaten).
Satiety is helpful in managing the "calories in" half of weight loss, but it's not an absolute must. Knowing when it's safe to ignore hunger and doing so when you've already used up you're caloric budget for the day is a huge part of successful weight loss. Basically same spiel with the "calories out" end. Working out can be fun (which is helpful because it makes you want to do it), but a lot of times it's not - but if you want to lose weight, you do it anyway.