The GVWR of 6600 lbs may not be a concern if you load your truck lite. I think the 2005 Tundras were the smaller size, and may not weight as much initially.
You need to find your actual tow rating for the truck that you have. You can probably call your dealer, give him your VIN, and he may be able to tell you the rating. Cab/bed configuration, engine, transmission, final drive ratio, and tow package options all figure in on the towing capacity.
Next, you need to make a couple of trips across some scales to see if you are within all of your limits. A pass without the trailer hooked up, weighing both truck axles is needed. Then a pass with the trailer hooked up, again weighing the front truck axle, both axles, the total of truck and trailer, and then just the trailer axles. Make another pass without the WDH hooked up, again weighing the axles and the total. These figures can give you all sorts of good information, and also let you know if your WDH is setup properly.
A CAT scale can give you these figures by weighing each axle separately. If you use the local quarry scales, you will need to record the figures as you weigh them....many quarry scales have electronic readouts that you can read from the drivers seat. If you use the local quarry, go in and get permission from the weigh clerk 1st, along with instructions.
Chap , DW Joy, and Fur Baby Sango
2006 Ford F150 Super Cab 4x4
2008 Surveyor 263