Hi, Welcome to Just Answer!
I am an American Board Certified Neurologist (studied & worked in USA) with a vast neurology clinical practice experience. I am familiar with the condition that you have described and can help you with your questions/concerns.
Cerebellum is the area of the brain that is concerned with coordinating body movements and maintenance of balance. If somebody has cerebellar shrinking then imbalance usually occurs.
Sometimes this imbalance itself may be interpreted as weakness or there may be other causes for weakness. Involvement of nearby brain structures like brain stem, other areas of the brain, or outside the brain in the spinal cord, muscles, nerves etc all can produce weakness.
I assume you had a CT or MRI of the brain, if that can explain for both your imbalance & weakness then no need for any further investigations from that perspective. On the other hand if only cerebellum is involved then you need a further evaluation as to find why there is weakness as well.
At that moment you will also require additional investigations like blood tests (CPK, LDH, ESR, Thyroid tests, B12 level), EMG test etc. If any of them are already done no need to repeat them.
Physical therapy is one of the cornerstones in the treatment of your symptoms. Unfortunately it is not helping. If the above investigations reveal something then treating such a condition hopefully will help you. Cerebellar imbalance may respond sometimes (not in all patients) with Tab Buspirone, Propranolol etc. You may start one of them at a small dose and up the dose gradually as required and as tolerated. You can get a prescription from your local Drs and also the dosage instruction.
If you haven't seen a neurologist at a clinic please do it now. They will examine you and see is it all balance problem or is there actual muscle weakness as well, and then decide whether you need more investigations (from the above mentioned list).
There are also conditions like MSA (multiple system atrophy), SCA (spino cerebellar ataxia), paraneoplastic syndromes etc that can present with shrinking of cerebellum. After the clinical examination if there is a suspicion of these possibilities then we will discuss what further special investigations are required to confirm those diagnoses and how to manage these conditions.
I assume there is no alcoholism (it is one of the commonest causes for cerebellar shrinking), also not on certain medications like dilantin etc that can produce shrinking of cerebellum (please correct me if I am wrong). If such risk factors are there then the treatment is avoiding the exposure to these agents.
If you need a more elaborative discussion on your case then please ask further questions and clarify all your doubts.
All the best!