GLLHG has done a superb job of answering the question.
I too am 6'3" and while I don't own a classic Morgan (yet!), I have sat in a 4/4 Sport and had the pleasure of an outing in Easter's Sport. My head sat a little proud of the screen and I'd be inclined to drop the seat to decrease buffeting (again, as per GLLHG's comments).
As for you weight, I'd 15 stone and while I found the cabin more snug than the Aero, it wasn't uncomfortable and would merely necessitate a slightly altered driving style (elbow out the top of the door!)
Are you geographically close to any dealers?
