Both, Gromit. If a dog was as much underweight as some are overweight, then the law would be on them like a ton of bricks...
Overfeeding a dog is a failure to take into account its needs, and can have dire consequences for its health. Joint problems and heart strain are just a couple of examples. It's not fair to a dog to overfeed it; as owners, we are responsible for all a dog's needs. It can't feed itself, so we feed it, and we need to ensure we are feeding our pets correctly. So it might look at you yearningly when you are tucking into your roast dinner; it's no excuse for giving scraps, leftovers and in some cases buying whole meals just for the dog!
It's not a case of meanness; I treat Jack, sometimes with cooked meat, sometimes with gluten-free dog treats (due to his "condition"!), but I balance that by feeding him less at meal times if this is the case, so he is still taking in roughly the same amount. He also receives daily exercise.
As robotics says, owners who overfeed their pets are killing them with kindness. I carry a little extra weight (!) and this is MY fault, and MY concern, because I am responsible for what I choose to eat. My dog isn't.
Great question :) x