Bike riding usually is one of the sports you can continue to do because you are not supporting your body weight on your legs. 

I happen to live near the ocean (I can walk to the beach) so I got into scuba diving a while back.   That is a sport anyone can do.  More then a few divers are obese and very round-looking but after they jump off the boat they become weightless in the water.    I good diver tries hard to not expend much energy and keep the breathing and heart rate as low as possible.  Even to the point of not moving the arm quickly to look at the wrist-mounted computer.  Every tiny motion uses up air.  Even breathing requires effort so you learn to do that slowly.