Load range - try moving to a higher load range (ie. higher max pressure) tire, if you have room.
Tire pressure always matters - it sounds like you are mostly running heavy, so I'd be going with the Max Pressure listed on the tires you have.
I asked for guidance on brands for the dual axle trailer I picked up this year:
http://www.tractorbynet.com/forums/trailers-transportation/229438-decent-non-china-trailer-tires.html
I wanted radials, but even amongst the "big names" out there, there is a lot of junk.
Did a run last weekend with new Greenball's on my trailer - about 2 hours each way. So far, so good.
Many (non-Ag) tires will deteriorate fast if parked on dirt (long term). Asphalt, concrete, deep gravel or even wood is a better choice.
Unless you are really sure of the weight, it might be worth checking on a scale that won't get you in trouble (local dump, friendly business.....). You may be hauling heavier than you think you are.
Brakes are working/adjusted normally ?
Rgds, D.