Have two of the 2004 - 8.1L - 3.73 4x4 burbs, both white LS models. My favorite! Had a 1994 with 5.7, still have a 1999 with 5.7 as my daily driver, just picked up a 2010 - 5.3 4x4 for the wife's daily driver.
The 8.1L burbs get 14 on the highway. Throw in wife and 7 kids, get 14 on the highway. Add rear cargo carrier and luggage carrier up top, get 14 on the highway. Town is 10 to 11 it seems, but we live in small town so mostly country driving. Tow burbs also live in front of trailers owning 4 suburbans, so mileage doesn't matter. But towing 10,000 pounds we usually get about 8 mpg in the midwest. When we went out to yellowstone, milage did drop to mid 6's with all the large grades. I am planning on putting 4.10's in one of them for future towing, I am right at the 10,000 pound tow limit and feel it with the 3.73
On the highway, I am limited to 65 mph to keep the RPM's around 2700 if I remember. OD just doesn't work there if you hit any grade and on an overpass it wants to hit second when on cruise. So I figure set the one with 70k miles on it up for serious towing with the 4.10's and keep the other one with 160k miles on it for local towing or the boat, which is only 8,500.
The 1999 definitely feels it when I tried towing the boat with it. But it gets 17 mpg on highway and 13 to 14 average driving.
The 2010 burb is what we refer to as the "eco-burb". It has the 5.3L with 3.07 gears and 6 speed. Only has a 5,500 tow rating, but got it for a glorified station wagon. Highway it can get 21 to 22 mpg. Then you go 75, add the wife, the 7 kids, luggage carrier on top and cargo carrier on back and you end up getting 17. I do not recommend these gears. The 5.3 is fine and the 6 speed, but it is not geared enough.
At the weight you are looking to tow, I would get a 2500 burb, 6.0L with 3.73 gears. I do not know the specs, but it would probably be up around 9,000 lbs, I forget if the higher number was with 4.10's or not. But my 2004 2500 burbs feel solid. Ride good, but solid. The 2010 1/2 ton is like a toy. It is lighter, thinner and feels like a station wagon. The 2500 in 2004 is a tank! If they still made the pre 2007 version, I would have bought one. Best burbs I have ever had.
Everyone I know who towed a TT over 5,000 pounds wished they had a 2500.