In my truck I once carried two pallet of sod, it was wet and weighed at least 2500 lbs. per pallet. Truck handles it fine. I once loaded it with over a yard of pea gravel, right at 4000 lbs., truck handles it no sweat. While I never worried about the axles, I was a little concerned about the springs. I found out later by talking with the previous owner, that the truck had heavier duty rear springs on it. That would explain why with two pallets of grass, it was on the overloads, but they still had a lot of movement left in them.
Try upgrading the springs first, these rear ends are pretty freaking stout. Only downside to my rear end is that it kept going through spider gears.