FWIW, I just weighed my rig this weekend. I'll put full stats up on a new thread in the towing forum, but here's the gist...
Truck: 2012 GMC Sierra Crew, 5.3 L (LMG), 2 WD, HD Tow (3.42)
Trailer: 2014 28BHBE (quite a bit heavier than your 26BH)
I'm right at the max on payload capacity with full fuel and passengers (we don't put cargo in the truck). Trailer weighed ~7500 lbs (yellow sticker says 7049), TW was ~960.
The truck tows fine at 60-65 MPH and gets about 8-9 mpg. I get about 16-18 while not towing in mixed driving.
My neighbor towed a similar sized trailer with a Tundra and got what he called "bad" mileage. I don't know the specifics like tank size or exact mileage for his truck, but on the exact same journey, he would be coasting into destination on fumes while I still have at least 1/4 tank left. He also complained about how his Tundra squatted. (he traded the trailer for a 5er and the truck for a 3/4 ton Dodge diesel after less than 2 years).
I know a lot of that was a bit subjective, but those are my experiences. If I were to go back in time (hindsight and all) I would probably pick up a 3/4 ton truck. While I love my truck, I would still like to have some cushion on my capacities. But I would stay in the GMC family for reasons previously mentioned on this thread; my second choice would be a 3/4 ton Ford, or possibly an EcoBoost with all of the max towing and payload offered in the model.
2014 Jay Flight 28 BHBE
2015 RAM 2500 6.4L HEMI, Tradesman 4x4, 3.73
Blue Ox SwayPro (BXW 1503)
Upgraded from an REI internal frame backpack and a Eureka 1/2 dome tent!