Not sure if this helps, or just makes it all more confusing, but my theory is that a greater weight load on a tire (or less air pressure in the tire would also create the same circumstance) does NOT change the circumference of the tire (the circumference is held firm by the steel belts in the tread, the belts cannot flex in a manner that would allow a change in circumference). What happens is the greater deformation of the tire's shape causes more squirming of the tread blocks right where the tread initially contacts the road, and then again where the tread leaves the road with each rotation. This causes more friction (and thus heat) and also has the effect of causing the tire to rotate at a speed something in between that of a non-deformed tire, and a non-deformed tire of the same radius as the deformed tire.
On the other hand, there will always be a tiny bit of give due to the flexibility of the tread blocks, even on dry pavement. It's just enough give so that things should not destroy themselves (not right away, anyway) if the truck is driven in a straight line on dry pavement in 4WD. It is not enough to allow for turns on pavement however, and this is generally where things will start to grenade.