Vaughn has the right idea. The tables I have seen from tire manufacturers say basically the same thing as what he said. Using round numbers may make it easier to understand.
If your tire is rated to carry 3000 lbs at 80 psi, then it can carry about 2000 lbs at 53. 3 psi, or 1500 lbs at 40 psi, etc. This is only good up to a point.
I would add a few extra psi as Vaughn does, just to be on the safe side. A little more pressure won't hurt, but too little pressure could kill you.
I can't get the entire table to copy here, but here's an example from one manufacturer's data, for one tire:
For a load range D tire, size LT 225/75R16:
35 psi = 1500 lb
40 psi = 1650 lb
45 psi = 1790 lb
50 psi = 1940 lb
55 psi = 2060 lb
60 psi = 2190 lb
65 psi = 2335 lb
Note that load range D tires only go to 65 psi.
For what it's worth, I have pulled a 14,000 lb fifth-wheel trailer with my 1995 truck for quite a while. Hitched up, the truck's rear axle is carrying 6050 lbs. This is well above the rated load for even most load range E tires. In spite of the load, my tire dealer fitted load range D tires after he couldn't get four Wranglers to run without vibration. He assured me that the D tires would handle the load, and they did.
I no longer pull that trailer with that truck, and would probably not accept load range D tires for that application again.
I guess the questions are:
Can you do it and get away with it? Probably.
Is it prudent? Definitely not.
I hope this is helpful.
Loren