I must confess I find it nice exercising on the weekends because I feel like I can take my time for it instead of cramming it into the day like I have to do on weekdays. But graduate students live odd hours...
In regards to injuries, I struggle with lower back problems due to pelvic issues. Having my girls a year apart screwed up my pelvis and I had a lot of major back problems as a result (for instance, the last month of Mary's pregnancy, I couldn't stand up straight and had to be wheeled around in a wheel chair if I had to walk any distance at all). Anyhow, I have found that Pilates is like physical therapy and I haven't had any back issues since doing Pilates regularly. It is amazing.
I really think it takes time to figure out which type of exercise works best when you have particular physical injuries/weaknesses to cope with. Have you tried swimming, Emily?
Regarding exercising for weight loss or not--My initial goal in working out was to finish losing the pregnancy weight (it has taken me 3 years...yep). Now, I am actually close to losing all my pregnancy weight, but that is no longer my goal. I actually work out now because I like how my body feels when it is strong and in shape. I suppose I work out for the endorphins now as opposed to for body image. I honestly like my body now. I haven't felt that way since pre-babies.