My parents need something that can be used for carrying an old, fat dog up the stairs at night; looking for something very lightweight that can carry around 100 pounds (80-lb dog + box to hold her). Any suggestions?

Due to the weight, you'll better off finding a (dolly) hand truck locally. Look at the bottom plate and make sure someone can balance the doggy box on it. Also given the wheels probably will be skinny, small and cheap, ensure the stairs aren't too high. Wrestling a heavy or bulky items up stairs can be a bite.