RT you got it.
Tires, followed by wheels, springs and axle capacity are typically the limiting load carrying factors in that order based on their individual ratings on 1 ton trucks.
Bout every crew cab diesel pickup has an empty rear axle weight of 3500lbs give or take a few....hundred.
So in your case you're good to about 7200 max with your current tires. 4000lb rated tires are easy to get but rim ratings are tough to figure out on OE rims, however if a truck comes stock with 3600-3700 lb rated tires I'm saying the rim is good for at least that much.
Like morsno said load it up and go camping. You're good with your choice.