Are you allowed to jog or run on Shabbos? How about in the weekday? doesn’t it say that one should’t since it takes away 1/500 from his eyesight?

One may not run or jog on Shabbos except for a Mitzva, for example to get to shul.

The Gemara says that even during the week, taking a long stride (more than an Amah between the feet) takes away 1/500 of one’s eyesight (except if for a Mitzva). The cure for this is to look at the Shabbos candles when starting the Friday night kiddush.