My 52 3800 weighed 4,400lb with me in it and has a steel plate in the bed floor about 3/16" thick ~300lb. I'd be surprised if another 3800 weighs much if any less than 4,000 lb.
I drove mine around for a few years on some very old bias ply 7.50-17 tires and it was a little stiff. Then changed to new 20 year old bis ply 8-19.5 and it was a whole lot smoother, perhaps because the tires weren't quite as old, perhaps the slightly taller diameter. I later put 8R19.5 on the rear and they also rode well. All were well rated truck tires and I ran 75-90 psi depending.
Personally I would use more than heavy enough tires to comfortably and safely haul a full load in the truck if you ever ended up doing that, after all it is a truck. The stiffer sidewalls should help it feel more firm in the corners, you can take corners pretty quick in these trucks, I've tried

Grigg