We have a 2011 Silverado with the trailer package and the tow rating is 9600 lbs so you should have no problem. Our best friends have the same truck and they tow a Jayco trailer with a dry weight of 7k with no problems. Good luck!!
BB,
BE careful of any towing guide that is not from the auto manufacturer.
Those limits they published are for vehicles maximum tow that have the proper tow package.
If there is not any tow package, it will be much less.
I have found too many mistakes or omissions in those generic listings to put it on this site.
Also, as mentioned before those 20" tires and rims will probably limit it to around 6500lbs towing.
Those tires do not have the carrying capacity.
Looks like you've got quite a bit of advice already. But I'll add my of experience to the mix. DH's parents had a 2001 Chevy Silverado 1500 Z71 - so it included a heavier suspension and towing package from the manufacturer, as well as some other things. They bought a 30' TT with a dry weight of 7200# and didn't look at any books for weights, just relied on the camper dealer saying okey-dokey.
I knew, from looking at our truck (a 2002, but otherwise exactly the same) that the max tow was 7000#. I pointed out the weight sign still above the door from the dealer to DH. They got the TT home okay. And took it on a few trips (loaded with gear) and complained LOUDLY that it was driving like there were gerbils running the engine.
DH said nothing, went to their truck and pulled out the owner's manual. He opened it to the correct pages and set it in front of his dad. They now have a 2013 Chevy Silverado 2500 HD and no more complaints.
My truck has the 3.42 and I would pull that trailer without worry, the Denali with the 3.73 picks up like 2000# of extra capacity, IMO if you have the 3.42 keep your foot out of it off the start and you should be fine.
If that is correct about the 20" tires, you will be at 6480 lbs for towing. I had estimated 6500 lbs for towing.
Not only that, if you find a trailer weighing 6480 GVWR, you can't put anything in the TV other than the driver.
You need to figure out how much weight you will put in the TV and subtract that from the max trailer GVWR.
EG; If you put three more people in the truck weighing 350 lbs and have 450 lbs of gear, you max trailer GVWR will be 5680 lbs.
That 7000 lb trailer is way too much for this TV.
I thought the tires would break the deal...
I always check several sources to see if they all are similar.
I don't like the 3:43(?) rear end ratio for a heavy trailer. 3:73 is a minimum for something that size IMO.
If he is towing a 7000 lb trailer and can tow 7000 lbs (if he has standard tires), he can put nothing but the driver in the TV.
No passengers, no nothing, nada in the TV.
The OP needs to calculate what he will put in the TV other than himself and deduct that from the 7000 lb rating to get his maximum tow rating.
FD,
3.73 is the "DEEP" so called axle on that truck not 3.42.
At least here in the US.
And we don't advocate towing over the GCWR or GVWR, no matter what a seat of the pants experience is.
2010 should have the six speed auto. While I think it should have used 3.73's it is the same gearing that GM/Chevrolet used for the 10k plus tow rated trucks. The six speed automatic changes towing drastically from the old 4 speed it replaces.
Moving on, depending upon bed length and cab size, the trucks with a tow package are upwards of 10k or so rated. IMHO though I think 7k is probably the limit. Give or take. Flat land, no prob; lots of hill climbing? Eh... Looking around on other forums I've read plenty of admonition to not exceed 80% of GCWR, and 7k is like around it. As it is you'll be finding out just what the engine sounds like at full song.
I can't comment on the 20" wheels though, nor a non-tow package setup; when I was looking this past spring I was looking at the base models but with tow. YMMV.