Having similar (identical) tires is of course by far the best.
Increasing the pressure in the back tires will not make them carry more weight, at least not appreciably more. The suspension of the trailer is what determines how much weight falls on each axle, not the tire pressure. The only ways that the tire pressure would affect things is by slightly changing the diameter of the tires (and hence slightly altering the geometry of the suspension system) and by affecting how the tires react to dynamic loads.