Question: link between overweight and loose stools in cats?

Im not looking for advice since the vet already knows and has given good advice. Im mostly curious if anyone else experienced this.

So I adopted my big 17 pound cat from a rescue. He was 1yr old at the time, and had loose stools. The rescue tried all sorts of things, but none of them solved the problem. He is very healthy by all other tests.

When I adopted him, I pur him a high end, high protein food designed for easy digestion. It did not help.

So, at his first vet appointment with my vet, the vet advised adding psyllium, which helped. And also told me he was overweight. So I put him on a diet. Where I decreased the amount of food slowly. ​ and, it worked. He is still a huge cat, but now with a visible waist and rib cage I can actually feel when I pet him. He moves better as well.

So a few weeks ago, I realized I was forgetting the psyllium.... and his stool was solid. ....

So my question is is there a link between weight in cats and messed up digestion, or did Big Boy just out grow it?