Why do the prescribe betaxolol ophthalmic and Diamox (acetazolamide) for the eyes?

Lower eye pressure. These are standard treatments for glaucoma - a condition in which the internal pressure of the eye is high enough to risk the vision. If you are getting these (or know someone who is getting them) then an eye doctor (hopefully a real one termed ophthalmologist) has seen you, determined the condition is present, and prescribed these effective agents to protect your eyesight.