I have read 2 archive articles about exercise (one specifically about exercise on Shabbat). I am trying to improve my well being through exercise. This includes both fat loss and muscle growth through lifting weights (barbell and machine weight). The trainer I deal with prescribes specific days to lift versus take off in order to promote the best results (e.g. Upper body one day, lower body the next, followed by a day off, etc.). Would such exercise be prohibited on Shabbat? It might include about 1-1.5 hours lifting weight.

Weight lifting is good but not for Shabbat. It has two main problems. One, it is a week-day activity (Uvdin Dechol) Second is the issue of prohibited medical procedures on Shabbat and exercising is included. (Shulchan Aruch OC 328; 42) Try to talk to your trainer how to compensate for you missing Shabbat, maybe Motzaei Shabbat is a good time.