I have heard all the opinions before and after going through a set of tires, I learned that "max air pressure is for the max load". If they are rated to 15,000 lbs. and you weight 15,000 lbs., then put in max pressure. If you have 12,000 lbs. then you should come down in pressure. The exact amount is not scientific, but if the tire says max pressure 50 psi and you are 10% below the max weight, then reduce air pressure 10%.
Go out for a day and look at the wear pattern of each tire. If it looks like you are wearing in the center come down 5psi, if the outer edge of the tire is wearing increase 5 psi. I have G rated tires and was running with 110 psi. A reputable tire dealer says that the tire can carry 20,000 lbs., you do not want 110 psi with a 13,000 lb. load. I am down to 80 psi and the tires show normal wear and less bounce.
Not all tires show load capacity in pounds. If your tires do not show pounds you may need different tires.