I just got a newish 2015 Silverado 2500hd 6.0, long bed crew cab 4x4. My last truck was a toyota tundra 4x4. The tundra 5.7 easily pulled my 8,000 lb Arctic fox 25r but the handling was too squirrel...
6.0 gas engine in a 2500 truck likely has only a 3.73 axle ratio.
If you go too much bigger with the tires, you'll be doing an axle gear change to make up for lost power with the bigger tires, to the tune of about $750 per axle.