While your claims are fairly popular, AFAIK there is no evidence to suggest that non-nutritive sweeteners cause weight gain in humans. They are highly associated with weight gain, likely because people likely to choose diet beverages are people who have difficulty with weight gain in the first place.
Murine models are not particularly generalizable to humans, particularly when it comes to diet and nutrition.
> Some researchers believe that artificial sweeteners don’t satisfy people’s biological sugar cravings in the same manner as sugar and could lead to increased food intake. Still, the evidence is mixed.
> The strong sweetness of artificial sweeteners may cause you to become dependent on sweet flavor. This could increase your desire for sweet foods in general.
> Some observational studies link artificial sweeteners to weight gain, but evidence is mixed. Controlled studies suggest that artificially sweetened drinks don’t cause weight gain and may even aid weight loss.
In general, they cause your metabolism to slow down, and make you feel hungrier. Giving them to mice on calorie restricted diets causes weight gain and lethargy in the mice.
Giving a subjectively identical amount of sugar to the mice (on top of the calorie restricted diet) causes less weight gain than the artificial sweeteners. (Because the mice stay active.)