It sounds like these two problems are independent of each other. Belching is usually related to gastrointestinal issues. Have you changed the diet recently or given new medication? Older pets can have issues with the GI tract as a result of other disease such as endocrine diseases, allergic disease and neoplasia. Bloodwork and radiographs would be recommended to help rule out some problems and all other concurrent systemic disease should be addressed. Symptomatic therapy may also be helpful in identifying the origin of the problem, like antiacids. Slow walking or exercise intolerance may be aging changes such as osteosrthritis or related to another disease. Please have a thorough physical examination and consider comprehensive bloodwork and radiographs. It may be helpful if you have a video of this “gutteral belching” for your veterinarian to see at the time of examination. Good luck.