It will really depend on the load rating of the tire. Your tires should tell you the maximum load at full inflation. The load range (D or E) is almost meaningless, except for the number of sidewall plies (stiffness. ) I feel comfortable running load range D tires, for the reasons listed below:
My 285's are load range D, but they are rated for 3,400 lbs at 65 psi. This gives me a total rear capacity of 6,800 lbs. Remember, the axle weight rating is 6,500 lbs. This load rating is higher than the stock tires that come with the truck.
So if your tires are rated at 3,000 lbs, then as the game show says, "You [the tires] are the weakest link. " But, if your tires are rated above 3,250, then the axle becomes the weakest link.
Based on my truck's front axle weight (4060 lbs) I have about 4,740 lbs of rear axle capacity before I exceed GVWR. Even if I go to 10,000 lbs, my rear axle would only need to carry 5,940 lbs. Thus, 2 tires capable of each carrying 3,000 lbs would handle the load. I suspect that your truck would have very similar front and year axle weights. If you tires indicate a load rating of 3000 lbs or greater, you should be fine.