What would cause right side muscle wasting?

Muscle loss. There are a number of possibilities...But more information is needed.... Where is the loss? Arm, leg, which muscles specifically. Nerve or root or spinal cord or brain problems can all be potential causes. I suggest you see a neurologist.
See below. One can see muscle wasting from problems with either the central (brain and spinal cord) nervous system or the peripheral nervous system (all nerves outside the spinal cord). Other causes of muscle wasting include conditions causing muscle deterioration (myopathies). It would be appropriate to see either a neurologist or a physiatrist (specialist in physical medicine and rehab) for this problem.