You can go by those very vague guidelines, or you can run some calculations...
I'm away from my truck, so I had to pull numbers from interwebs. The heaviest listed curb weight for our trucks is 4528 lbs.
The max payload is 1581 lbs. Add those together and get 6109 lbs. Split that between four wheels and get 1527 lbs/wheel.
A SL-rated (112 load index) P-series tire has a load rating of 2469 lbs at 35 psi. A XL-rated (116 load index) P-series tire has a load rating of 2756 lbs at 40 psi. Either one of those way more than covers the theoretical max load of 1627 lbs per wheel for our trucks, especially for what the OP said his intentions were - he's not high-speed desert pre-running or adding air bags and packing a payload-exceeding camper.
As for tire weights, I took a quick look at the Falken AT3W specs, as I'll be getting a set of those soon. The same exact tire sizes, in P-rated versus LT E-rated, adds 6-7 lbs/tire to go to the LT E-rated version. That's a 15% increase, and there is no way in hell that increase doesn't adversely impact gas mileage.
Unless aired down tremendously, E-rated tires suck on rough rocky terrain. Been there, done that.
I don't want to get into a debate over this, as I've learned long ago that no matter what you write, somebody is gonna insist they know better, and will want to 'debate' it til they convince you. I'm not interested, so I will answer your post once, then let it go.
Firstly, EVERY model has its own weight rating, i.e. two different manufacturer/model 'C' rated tires could vary as much as a couple hundred pounds or more. Manufacturers list these specifics for their individual tires on their websites.
This therefore is the best place to find out the CORRECT INFO
on the tire(s) you're interested in.
As far as P-tires on trucks is concerned
The main reason why I stay away from 'P'assenger rated tires on my truck is being designed for passenger cars, they don't have any over-load designed in. For that reason, you need to deduct around 10% of their max rating when using them on SUVs/Vans/TRUCKs.
LT tires DO have over-load(reserve) built into them.
If you drive a pickup and use it as it was designed to be used, then you should use LT tires end of story. Contrary to what you seem to think, that doesn't mean E rated or 10-ply-although the extra '6-7lbs'ea/24-28lbs total added weight certainly doesn't add up to a noticeable loss in mileage . Not with the HD's, and not on my Colorado 2.8L. Both motors have more than enough torque to alleviate the extra 28-whopping-pounds, provided you're not running said tires at uber low pressures. What can alter mileage quite easily, is dumping air pressure.
I run mine around 55psi, and they've never cost me any mileage
As I said in my earlier post, LT's also come in 'C' and 'D' ratings, but in any event, they're designed to be used on trucks, thus carrying and towing extra weight, and some models add an off-road capability as well.
I've spelled it out quite clearly I think, in BOTH of my posts.
I can't make it any more clearer, and I'm not interested in debating the issue.
Good luck to the OP with whatever tires you choose.
i'm mooooovin on