You may need to replace the tires along with the truck. Unfortunately your configuration is likely to be significantly overloaded when camping. Based on the information that you provided it is impossible to determine whether your wheels and tires (especially the rear) are capable of carrying your super payload.
Max. tow limits are usually meaningless for most towers. What matters is payload and tongue weight. The published payload for this vehicle is 1760 lbs. You'll have more than 1.000 lbs. of tongue weight (note that this will be MORE than the limit of your vehicle). By the time you add all of the options you'll want on the Tahoe, your fancy Hensley hitch (190 lbs.), several passengers, your gear, several generators, your cooler, your dog, etc. you'll be grossly overloaded in this vehicle. You'll likely be exceeding BOTH your maximum payload and your maximum tongue weight (plus the rear tire's and possibly the rear wheel's rating).
You should be looking at a 3/4 ton truck to handle your setup properly and safely. 2013 Suburbans are available in a 3/4 ton (2500 series) configuration. If you have to have something new you're pretty much stuck with a 3/4 ton pickup (or higher).
Unless you travel SUPER LIGHT and pack every part of your load in just the right location then you really owe it to yourself to rethink your TV. Others here will say that they've done it for 50 years. I say they sure have been lucky. Someone new to towing doesn't want to be operating in the red before they've even left the driveway.
Run the numbers. The numbers never lie: