When you neuter a dog does it get fat?

Not necessarily. The testicle produces testosterone, which shifts the body towards building muscle and away from building fat reserves. When the testicles are removed during a castration surgery, this push towards muscle building is removed. If you don't maintain your dog on an active lift style and manage his food intake, he can gain weight more easily after being castrated.

However, if you feed the appropriate amount of calories (which includes both his dog food as well as any treats or scraps) and you keep your dog active, there's no reason why he can't stay as lean as he is now.