Can reading damage your eye sight over time?

Absolutely not. The eye's sole purpose is to provide vision, and it is essentially a "solid-state" video camera. Its parts do not wear out with use. Although there are diseases that can cause damage to the lenses (cornea and lens), film (retina), or "video cable" (optic nerve), they are not caused by over-use of the eyes. So use them to your heart's content!