Unless I am misunderstanding your point and you're saying there's evidence supporting the negative effects of non-sugar sweeteners for obese people, isn't this a classic case of correlation vs. causation, where observation X is seen as "ample evidence" of causation while it's merely correlated?

The kind of person that'll happily drink a bucket of soda (diet or otherwise) is likely the kind of person that has an unhealthy relationship with food in the first place, with a stomach (appetite?) capable of ingesting a lot of food and liquid. Which is a category morbidly obese people fall under.

Can you show us such evidence?