does change the metabolism of companion animals, so in most cases, they do not need as much food to maintain their weight as unspayed/unneutered animals. The problem is not with the animal it is us. We just tend to overfeed our pets and neutered/spayed dogs and cats are more apt to put on weight because of that.
As for laziness, again, the amount of exercise and activity of our pets is often dependent on us. If we do not give them opportunities for play and exercise, they can become couch potatoes just like some people. Many spayed/neutered dogs are field dogs, are entered in agility shows, become service dogs or are trained in search and rescue. These dogs are anything but lazy. Cats can get lots of exercise with toys and 'chase' games. Some cats love to walk on a leash with their owners. Try it!