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.
http://www.justanswer.com/neurology/54wua-severe-imbalance-been-told-caused-shrinking-cerebellum.html
There are many types of cells that make up the cerebellum. The most important is called Purkinje cell, which gives out information from the cerebellum back to the cerebrum and also to the brain stem and spinal cord. Loss (death) of the Purkinje cell is the most common finding in cerebellar ataxia from any cause. The absence of a functioning Purkinje cell causes the cerebellum to shrink. This shrinkage can sometimes be seen through magnetic resonance imaging (MRI) scans. The Purkinje cell is quite sensitive to decreased blood flow, alcohol, and other toxins, including some medications. It is also sensitive to heat stroke.
http://www.ataxiacenter.umn.edu/aboutataxia/cerebellum/home.html
Differential for CA: The differential diagnosis of later onset cerebellar atrophy can be hereditary, acquired, or degenerative. The acquired forms can be arrested or even treated and thus should be investigated. The investigation usually includes blood and possibly 24 hour urine evaluation.
https://www.healthtap.com/topics/cerebellar-atrophy-prognosis
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.
http://www.justanswer.com/neurology/54wua-severe-imbalance-been-told-caused-shrinking-cerebellum.html
Diffuse cerebral and cerebellar atrophy are neurologic conditions manifesting with different symptoms. Here is a list of these symptoms. slide 1 of 4. Cerebral atrophy denotes the wasting away of the cells and tissues inside the brain. In cerebellar atrophy, the cerebellum is the part affected by shrinkage. Patients suffering from diffuse atrophy can present with many debilitating symptoms. A typical condition where diffuse cerebral atrophy and cerebellar atrophy are seen is in cases of Creutzfeldt-Jacob disease.
http://www.healthguideinfo.com/neurological-disorders/p78656/
Hypotonia: Poor muscle tone or hypotonia is another manifestation of cerebellar atrophy, that can affect the posture and movement of the person. Intention Tremors: Involuntary trembling of the hand when pointing or reaching an object, like a button or doorbell, is a typical example of intention tremor.
http://www.healthguideinfo.com/neurological-disorders/p78656/
Dr. Benjamin Solomon Dr. Solomon. Yes, but...: Cerebellar atrophy is potentially a huge subject and can't fit into 400 words. Google cerebellar atrophy with NIH or emedicine or wiki to find good articles on the subject. A common cause in our society is long-term alcohol use.
https://www.healthtap.com/topics/cerebellar-atrophy-prognosis
The cerebellum controls such functions as subconscious skeletal muscle movements, balance, posture, coordination, and muscle tone. Conditions that can afflict the cerebellum include shrinkage of the cerebellum, changes with aging, genetic disorders, tumors, stroke, toxin exposure, trauma, birth defects, and infection. The following organs are closely related to the organ: Cerebellum: Brain stem.
http://www.rightdiagnosis.com/organ/cerebellum.htm
2 doctors agreed: Shrinkage: The cerebellum is a posterior area of the brain important in balance and coordination. Atrophy implies this area is shrinking in size. Some causes could include alcohol abuse, hereditary spinocerebellar degenerations, and chronic ms.
https://www.healthtap.com/topics/cerebellar-atrophy-prognosis
Descriptions of Cerebellum. Cerebellum: The portion of the brain in the back of the head between the cerebrum and the brain stem. The cerebellum controls balance for walking and standing, and other complex motor functions.
http://www.rightdiagnosis.com/organ/cerebellum.htm
what causes a shrinking cerebellum
A shrinking cerebellum can be caused by Alcohol abuse, hereditary spinocerebellar degenerations, and Multiple sclerosis.  A shrinking cerebellum  causes Alcohol abuse, hereditary Spinocerebellar Degenerations, and chronic MS.