Vision plays a huge role in balance. If this surprises you, try standing at your kitchen counter with your hands hovering over it and close your eyes. Feel like you are swaying more than when your eyes were open?
Your eyes help your brain understand where you are in space. When you eliminate this input by closing your eyes (or when your eyesight is impaired), you are forced to rely on other systems to keep you steady, which may not be as strong.
Make sure your prescriptions and lenses are up to date and schedule regular visits with your ophthalmologist to keep your eyes healthy and your vision sharp.