There is another plausible causal mechanism: weight gain flowing from hunger/metabolic dysregulation. This dysregulation being caused by some "factor X" which also causes other problems.
GLP-1 then addresses factor X, and the problems it causes, including weight gain.
Not that obesity doesn't independently cause problems but very plausible causality runs more than one way.
I would use the word "possible", not "plausible". GP's scenario is plausible since it doesn't need positing an as of yet unknown factor X.