I always did active stuff when I was obese. Not kickboxing, but biking, figure skating, lifting weights at the gym, dancing, etc. I think it's all doable as long as you accept you may not be as good as it as you would if you weighed less.
P.S. Bikes do a lot for your core and they do *some* for your arms because you need to hold yourself up on them. Well, you do if you don't get a recumbent!