They outright state this. The first directly says that their higher sugar substitute group had a higher BMI, lower activity, less fibre, and so on.
"To address your point: Potential for reverse causality cannot be eliminated; however, many sensitivity analyses were computed to limit this and other potential biases"
I've actually read the study (given that certain sorts cite it constantly), and do you know what "limited" that bias? Nothing. Literally nothing.
It is a correlation study. People with weight problems are more likely to utilize sugar substitutes. Reversing the causation is the root of an enormous amount of idiot science, though.
And just to be clear, researcher who post this bunk know exactly what they're doing, and usually it is to yield a "more research should be done" conclusion. It's when laymen start building their little notepad.exe listing of everything that supports their nonsense that it becomes a problem.