The frame, springs and brakes are the same in the 3/4 ton or 1 ton. The only difference is the extra leaf spring in the 1 ton, and the tires. So upgrading the tires does indeed get you more load capacity, maybe not "technically" but in the real world.
I agree Bogger, if you look at your GAVW for the rear it is listed at 6084lbs. If you look at your tires, the P245 load range E is rated at 3042 lbs. The weight rating is based on the tires, and the weight that they will handle. If you go to the P265 tires, load range E, they are rated at 3400 and some change. The tires and the load they can handle is what limits the GAVW of the vehicle. Keep in mind that does not change the limit as far as the weight you can pull, but does change the load you can put in the bed of the truck. I am sure there are some that will disagree with this, and they are entitled to their opinion. But you can look at any truck out there and you will see the load limit is exactly the load limit of the tires.
Those that seem to think a one ton can haul so much more based on brakes, axles and so forth, in my opinion are off base. I have done the research and all of the part numbers for all of those components are identical between the 2500HD and 3500. The only difference mechanically is, as you said, the 3500 has an extra leaf in the springs and they have 4 tires. Therefore they can carry the extra weight, but even the 3500 is limited by the combined load capacity of the tires.
