I don't think you are overreacting to be concerned about this - you know your dog best so if you see something that is troubling, then it deserves attention.
I agree with the above posters - more information is needed to provide better advice. The age of the dog is really important. Certainly bullies, like everyone else, get slower with age but stiffness and lack of playfulness in a younger dog can be signs of something that may need to be address, like hip dysplasia.
But you're doing the right thing is seeking advice on things you think are out of the ordinary, especially orthopedic issues and lethargy!