It is really too bad that tire manufacturers do not provide good load pressure tables for the smaller tires. They are pretty good about doing so with heavy truck tires. I have learned over time to extrapolate a ideal pressure for tires based on loading. If you notice, most smaller tires, like those on trailers, will show a max weight rating also. The max pressure is for than max loading. It is not the best idea always to run the max pressure just because it is what the tire is rated for. For instance, my semi truck, the drive tires are rated for 120 PSI. But the load pressure tables from Michelin show that, based on a typical 34,000 lb set of drive axles, the tire pressure for the 445/50R22.5 tires I am using should be around 95 PSI. Must be right, as I got 447,000 miles out of the last set, they still had 8-9/32 tread left, nice even tire wear, and the dealer gave me $150 each for them. I have taken the same concept and extrapolated pressures for my 3/4 ton pickup tires. OEM says run 60 front, 70 back. I run 55 all the way around when empty and only inflate more if I know I will be loading it down significantly. Tire life is great, ride is much better, and even mpg improved slightly because of less rear wheel "hop" on bumpy roads due to OEM recommend pressure.
Trailer tires, take a look at the total weight rating of the tires, determine what actual weight they will be having to deal with, and adjust accordingly. Tires need to absorb road shock that would be transmitted to the suspension, and a proper footprint needs to be on the ground to ensure best wear, best handling, etc. Too high of pressure for the load and uneven tire and suspension wear can be a problem as well as a reduction in performance on wet roads, braking (if trailer has brakes), etc. It is a balancing act to some degree. One doesn't want too low of pressure as sidewall flex can be extreme, but being rock hard is not good either. One of the best ways I have seen to determine the proper pressure is draw a chalk line across the tread, from side to side, on the tire then drive it a few revolutions. Check the chalk mark. More wear in center, then over inflated. More chalk wear at edges, under inflated. One wants a nice even wear across the entire chalk line, and that is the correct inflation for the load. Do that with a max rated load on the trailer and determine a good pressure for that application.