Allowing belly rubs is a sign of deep trust from a cat you didn’t raise, or a sign of a comfortable, secure cat with no doubts about the safety and continuation of their home and family. It’s a no-no for strangers to the cat, but if your cat is letting you, it’s a sign of the secure bond between you two.
The cats I raised from kittens will roll onto their backs and stretch for belly rubs when I walk into the room, but the cats I rescued are less enthusiastic about it. They all have grown to let me rub their bellies, but the one who lived outside before rescue would only ever roll onto her side tucked against me so my hand moved onto her belly, and the one from relatives will expose his belly but grumble about me petting it.
How frequently do you change the dog’s water?