Determine the axle rating for the trailer. The tire rating should, at the recommended inflated pressure, equal or exceed the axle rating.
The OP has a 2010 Flying Cloud (per his signature) and the 2010 parts manual stated it came with 3,800 pound rated axles. In a perfect world, each tire would need to support at least 1,900 pounds.
In weighing the individual wheel locations on our 2013 25FB, which also had 3,800 pound rated axles, we have found that there is one tire that carries nearly 200 pounds more than the others. The 25 FB right rear had the most load. The Classic had three at nearly the same weight and the left rear was lower by 150 pounds partially due to the removal of the water heater with 6 gallon storage capacity tank.
While the total weight of our Classic camping ready was 9,261 pounds, the two 5,000 pound rated axles were supporting 8,064 pounds. Thus, the factory installed Load D Goodyear tires rated at 2,540 pounds each had adequate load capacity with nearly a 25% reserve.
So the issue on lighter Airstream trailers may not be Load D versus Load E, but the quality of the materials used to build the tire and proper inflation at all times.
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TV - 2012 Dodge 2500 4x4 Cummins HO, automatic, Centramatics, Kelderman level ride airbag suspension, bed shell
2014 31' Classic model 30 twin beds, 50 amp service, 900 watt solar system, Centramatics, Dill TPMS, disc brakes, 16" tires & wheels