I had a skin only tummy tuck (no muscle repair and no lipo) . Can I go back to the gym at 3 weeks post op?

If your doctor agree, you might start doing something very mild, like just walking, or bicycling without any resistance, and listen to your body, if your body tells you to stop, stop. If your body tells you to rest, rest.And if you fee all right then you may increase the strength of the exercise little by little.Dr. Cardenas

I don't recommend that to my patients because 3 weeks it's not a proper recover time. Actually I tell them to wait 3 months. All doctor have their own opinions so I would suggest you to call your palstic surgeon and ask him/her if you can go back to the gym. 

We do not consider a surgical incision "healed" until approximately 6 weeks after surgery, due to the time it takes for collagen, the protein that holds wounds together, to be well established and secure enough to handle the stress of stretching during vigorous exercise. That being said, I often let my patients return to exercises earlier if there is no tension across the incision while performing the exercise. For example, riding an exercise bike is a great way to keep your legs in shape and not stress your abdominal skin. Please speak to your Plastic Surgeon about their thoughts on exercise after your surgery.