I'm no expert, but I can take a stab at it and pass along advise I've received.
Just put new LTs on the truck yesterday since we are taking a cross country trip in a few weeks and the rears were getting a bit old and worn.
The "tire expert" at discount I was shooting the breeze with basically told me when under load to run them at basically their max since they hold the most weight when they are full.
The 2500's door sticker calls for 65 in the front and 80 in the rear which is what I keep her at all the time. Is the ride a bit rough at times? Sure, especially when unloaded.
Tires with less pressure have more contact area with the road and provide better grip, but more rolling resistance which reduces mileage. Theoretically, at least.
Since the bed is pretty light just by itself, reduced pressure when unloaded isn't necessarily a bad thing as you may want that grip and better ride at the cost of a bit of fuel. My truck is basically a work horse though and when she's out and about she's usually hauling something so I keep her at 80 in the rear all the time.
Since the front isn't really affected much when towing (other than maybe lifting a bit when the trailer bears down) I find that keeping the front at the recommended 65 is just fine.
If I had any advise, it's to increase the pressure before loading up. What you do unloaded is all personal preference, unless you run way to low pressure all the time then you're contributing to premature wall failure and such.
Again, I'm not a tire guy and most of this is basically hear-say. Feel free to correct anything that's incorrect or misleading, won't hurt my feelings.