There is no doubt about it. Truck campers are heavy and most of us are probably close to the load capacity of our trucks. When it comes to load capacity, the limiting factor is often the tires. I k...
Yes, an LT tire is safe at rated capacity if you are maintaining a reasonable speed around 60mph. Cant' find it now, but from previous research, I believe they are tested at 55mph.
If you go up two sizes, usually you can gain a couple hundred pounds of additional tire capacity. You would need to verify the rims are capable of the higher capacity as well.