His tire, the Federal Couragia in 37x12.5x20 is an E-rated tire. With 3750 max load at 65 psi.
37X12.50R20LT
25 psi 1930
30 psi 2225
35 psi 2470
40 psi 2705
45 psi 2925
50 psi 3085 (D) 120
55 psi 3335
60 psi 3525
65 psi 3750 (E) 126
The average front curb weight is 2765, and average rear curb weight is 2252. I don't believe you should be dividing that number per tire, but this places your front tires between 35 and 40 psi, and your rear tires between 35 and 30 psi.
Now take into account the cold and hot tire pressures, where they typically increase on 37's by 5 psi when hot. I would keep the psi on the rears at 30 psi, and the fronts at 35 psi cold, so when they heat up, they're in range.
This is exactly what I'm doing with my 37's, not the exact pressure because my are D rated and on 17" wheels, but I follow the same charts to start with. Then I do a chalk test, and it's usually spot on.
When you're driving a heavy duty truck, with more weight, then you'll inflate to a higher psi to accommodate for the increased curb weight... or if you're towing in the rear for the increased tongue weight. However, these tire inflation charts from the manufacturers have never steered me wrong.
I would say if you're inflated to 40+ and when your tires heat up, you're psi is probably bumping the 45 psi and higher, and is over inflated. There's also a tire load carrying capacity number that speaks to very specific psi. That would suggest on a 120 load index that the psi should be 36 psi for the front and 29 psi for the rear, but again a chalk test would be a good indicator.