Here is a formula I picked up somewhere years ago; it was represented as the correct way to determine the needed pressure, I can not say it IS correct, but it matches pretty closely with the inflation schedule that came with my truck
Actual weight on tire (I just weigh the axel and devide by two)
devide that by the max. rated weight for the tire and multiply that times the max. rated pressure for the time.
In my case;
front axel weighed 4650 on DOT scales, that devided by two gives me 2325, which when devided by the rated capacity for the tire of 3415 gives me . 68. Multiply that be the max. pressure of 80, gives a correct pressure for that load of 54. 46 psi. (I usually fudge up a few pounds and round that one off to 57 #
The schedule that came with my truck gives a weight capacity of 2400 # at 50 psi.
Vaughn