[disclaimer]I appologize ahead of time to any engineers on the board for the following slaughter of physics terminology[/dc]

The weight plays a role; but the size does as well. As the axle is pushing on the tire in one direction, the friction coefficient of the surface its sitting on is providing some level of 'push' in the other direction. The 36" tire will create a larger lever arm and thus increase the torque "felt" by the drivetrain when one of the tires is wedged in a hole.

The combination of size and weight is an issue as well. Assuming the tires weigh the same amount and are spinning as the same speed, the 36" tire will require about 20% more force to be brought to a stop by the surface its touching due to the larger lever arm mentioned above and the tire's tendency to want to remain travelling at the same rate. The 36" tire likely weighs more; so that factor is increased. If both a 30" tire and 36" tire are spinning in the air and then come down on a surface with enough 'grip' to bring both to an immediate stop, the shockload experienced by the drivetrain will be greater with the larger tire.

http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html