The picture isn't ideal to reference from, but making some estimations:
About 65% of the chipper's weight comes off the back axle.
Deceleration force of 1g would take another ~12% of the chipper's weight off the back axle.
Assuming the truck weighs 8klbs with a 50/50 split and chipper weighs 3klbs, the combo weighs 11klbs.
The front axle, with the chipper attached and the vehicle at rest/no acceleration on level ground sees about 8950lbs while sitting still. The back axle still has 2050lbs.
While stopping with 1g of acceleration (a general best case situation), that would shift another 360lbs from back to front leaving the split being 9310lbs/1690lbs.
Assuming the box is equally filled, and excluding the "mother's attic" over the cab each pound squirted in the bed is puts ~.15lbs on the front axle and .85lbs on the rear. So 8klbs of material in the bed would make the split 10510/8490.
Probably sucks to drive empty in the mud.