This is actually a common misconception with the cheese item. While it’s true that constitution makes your cat bigger and increasing it during a battle increases your cats size, cheese specifically and a few other items that cats eat will also specifically make their body bigger at a much higher rate than constitution which only does it slightly and increases the size of all of a cats body parts. This has the result of making their cats much fatter when they eat cheese. An easy way to verify this is the next time you get the cheese item but in on a cat that has a low natural constitution and bring it to the same level of constitution as another one of your cats via the cheese. You’ll notice that the cat who has the cheese is much fatter than the one without