I have a 1996 C1500 with a 5.7L vortex and 3.42 gears. MFG max rating was 6500 pounds. I had it weighed, added a tranny cooler and larger radiator. My TT weighs about 6300 pounds and it pulls nicely.
Would I take it over mountains out west? No, does it do well from here (KY) to Florida?, yes.
If you have the money and you want a larger TT or fiver then spend the money on a 3/4 ton or more but if you are on a budget get a TT sized that you can add 1000 lbs and be below your max combined weight.
My tranny is a 4l60E by the way.
Just size your TT appropriately