Well, from that link

In addition, the researchers reviewed a study in schoolchildren that showed an educational program advocating fewer sugary sodas reduced weight gain and obesity among the kids after 12 months.

Which you would expect if the sodas had a causal relationship with obesity, and probably not if they didn't.

See also this article.

Can you think of any observations, in humans, which favor the LPS bacteria model of obesity, rather than simply being reconcilable with it given enough ad hoc additions?