I see no reason why you could not exercise. The precaution may have been suggested in order not to harm the good eye with certain activities, such as tennis, handball, basketball, etc. If you engage in any activity where there is a possibility of something hitting the better eye, you must wear eye guards. In fact, you should probably do this as a routine anyway. I do not know if you wear contact lenses to correct the aphakia, or if intraocular lenses (IOLs) were implanted at the time of the cataract surgeries. However, either way, eye protection is a good idea. Have your ophthalmologist perform a complete dilated retinal exam, to be sure there is no need for prophylactic laser to any weak or thin areas. If not, then I feel you are able to do aerobic exercise (walking, elliptical, stationary bike, swimming), and weights.