Why might a 9-year-old Jack Russell be losing weight?

There could be many reasons. I recommend you take your dog in to be checked out by your Veterinarian. Bring in a sample of his feces too to have the Vet check for internal parasites. Are you feeding a good name brand dog food? Don't feed cheap store brands. The main thing is that your dog should have a good check up done by your local Veterinarian.