I have a 2013 Tundra 4wd TRD 5.7L. I have a 10K lb Equalizer hitch and tow a 7,600 lb travel trailer that is stickered at 6,200 dry weight. I've weighed it many times and the tongue wt always comes out around 800-850 lbs.
You said the Tundra payload was 1,600 lbs but you might want to check that by weighing the truck and comparing to GVWR. After truck options, mine had much less payload than that.
I'm getting 9 MPG consistently over 1800 towing miles, and it seems more related to speed than hills or weight. Under 63 or so and mileage is good, over 65 and it drops like a rock.
The Tundra does an outstanding job of towing this load and we are pulling it from Alabama to Utah in late May (4K miles round trip). I'm 400 miles from a factory-trained Equalizer technician and continue to play with the WDH adjustments. Have made arrangements with a factory-trained tech in Oklahoma to adjust it as we go thru there.