If you are looking at new rims there is no reason not to look at 17 and 18 inch rims. Much easier to find a 8" wide 18" rim than for the 16". Even my factory forged aluminum rims at 17" are 7" wide which limits my tire choices as many specify a 7.5" minimum. If you alter the profile the overall tire height will be little changed with the larger rim diameter.
I have a 2011 GM truck and that year GM changed the bolt pattern and even 3 years later few wheel manufacturers make ones for the new GM heavy duty trucks and designed for carrying 3800 or more lbs.
