Your height wont be a problem, i am 6'1 and also can fit pretty comfortably in a flat kart, you can move the pedals farther forward and help give you some leg room, although i cant really use a steering fairing like some can because my knees keep hitting them when i had one on the kart and it tore up my knees. Your weight will be a bit of a disadvantage, but you can run the super heavy and sumo classes at some tracks, which are both specifically for drivers that cross the scales at over 200lb driver only weight. As far as setting up the kart with all the weight on the left rear, you can get around that by moving your seat as far forward and to the right as you can get it, to help balance out the weight a little bit. It is definately a challenge but im sure you can get it figured out. The info given to you above is all great info and will help you out alot if you follow his advice. Everything was spot on.
As far as finding a seat that fits you, you can contact any of the seat makers and they can make you a custom seat that is tailor made custom fit for your body if you need one, and im sure it wouldnt cost much more if any more than a regular seat would cost you. I would talk to Jeff at Comp Composites about making you a custom seat if you choose to go that route, he would help in any way he can and can make you a seat fit specifically to your size and measurements to give you the most comfortability you can possibly get.