krewzlo
+1y
I have always been concerned too about load rating on tires for my 19's and even the low pro 16's I used to run. There is more weight on the front tires when not towing a bumper tag trailer than no trailer at all because of the tongue weight is actually taking weight off the front end as the rear axle acts as a pivot point, kind of like a teeter totter. A gooseneck trailer will put some extra weight on the front as usually the ball is like a inch ahead of the axle as I remember. With the rear axle taking the grunt of the weight you are spreading that weight over 4 tires, so I never worry about the rear being overloading the tires, unless you are pulling something you shouldn't be. The stock hitch on my 2000, is only 10,000 with weight distrubution bars, and that is only 1000 lbs tongue weight. I don't know the gooseneck ratings for the truck but I would imagine it wouldn't be over 12,000 lbs as my 07 diesel max's out at 14000lbs gooseneck rating.
All in all I am more worried about the front tires than anything.
If you are running 16's the 225/75/16's d or e range will clear on a 5/7 drop if you roll up the fender lips in the front, but as far as 19's there isn't much options for anything close to a d or e range tire. Anything bigger I am not sure, but I can't imagine there is anything that would fit that is a LT tire.