Car tire pressures are higher front or rear to handle the weight of the engine and a full load of passengers at freeway speeds for extended periods of time. Uninflatting is likely to cause a tire to overheat and suddenly fail.
With trucks the tire pressures recommended are for a full payload in the bed and with a full load of passengers in each of the available seats in the cab. Heavy duty truck tires are not the same as car tires by any stretch of the imagination. The idea of adjusting the tire pressures to match the load is a stupid one at best and actually dangerous as the end result will be underinflatted tires.
With my tires that are 3750@80 PSI and no load in the bed they each support 2400 lbs. so according to a tire chart I would inflate them only to 55 lbs of pressure. If I do that the tire wear will be much greater on the outer edges of the tire and there will be less contact area on the pavement so longer braking distances and there will be more sidewall flexing which also affects road handling.
Start with the sticker pressures recommended by the truck manufacturer and monitor the tread wear on the front and rear tires. If it is uniform from edge to edge then it ain't broke and no need to fix it.
Tires are designed to allow for increases in internal pressure as the heat inside the tire warms the air and causes it to expand. When the tire pressure is measured with the tires "cold" all it means is that the air temp inside the tire is the same as the air temp outside the tire which is the baseline.
Tire pressures do increase with speed which is part of the reason why tires have a speed rating. Tires for my coupe are rated for 125 MPH and I could buy ones for a lot more money rated for 140 MPH and that is sustained driving speed. The tire dealers will not sell me a tire for my particular car that is rated at less than 125 MPH even though the speed limit is at most 70 MPH in my state.