Well, smoke, I think, is basically particulate matter mixed with air, so that particulate should have some mass independent of the air it's mixed with.
I suppose you could load a pipe, weigh it, and then smoke it to the bottom without dumping any of the ash. Weight it again afterwards and you would have a rough idea of how much mass had been lost through the burning process. Although I would guess most of the weight loss would be from the water which was evaporated from the tobacco.
Still, it would give you a starting point.