Well, he does have gout, of course. He could be trying to relieve pain in a toe or something. I think that's why he sways when he's standing, most noticeable when he's holding a camera.
(And related to that, if he does have back pain, either from some accident or sitting in an awkward position in an old love seat, I think his rocking back and forth is to relieve pain as well).
Let's put this rumor to rest: he doesn't have gout. He claimed his foot was hurting and everyone online jumped to the conclusion that it was gout and he didn't deny it. He's shown a photo or two of his foot when it was hurting and it didn't look like gout. He hasn't experienced any other subsequent gout-attacks (for lack of a better phrase) since this episode and he eats like complete shit.
He does not have gout. It's a funny meme that pisses him off but he does not have gout.
He claims he has a bad back and this is more debatable. Because the development with him swaying back and forth is relatively recent (in the last year or two that is). He's never displayed a back spasm or anything like that in the thousands of hours of video footage of him sitting on his ass. And there's never been footage of him being in pain and playing while lying on his back like most sufferers of back pain would do.
I personally believe he doesn't have a back injury. He may have suffered a sprain when he had the car accident but that was it.