Not only is it unfair to the character of Gimli (a helpless and unwilling victim in the hands of the screenwriters), but it's also unfair to the audience. My sense of humor extends far beyond belching and drinking.
I didn't mind Gimli sitting in the Steward's Chair as much as I mind the comic relief Gimli, but I agree, it's still out of place and doesn't really make sense if you think about it. It's unlikely that Aragorn would have allowed it.
If anyone had the right to stand on Balin's Tomb, it would have been Gimli - not that I think he should, or would have in ordinary circumstances. If you think about it, Gimli was only standing on the tomb in order to protect it, to kill any nasty goblins that dared approach it or defile it. Not only that, but he was putting himself in the center of the battle, exposed, for the sake of Balin's Tomb. So, I would argue that Gimli was in fact showing a great deal of respect (in that case), and perhaps more that Balin would have expected.
