More power

A 2011 Silverado with the 5.3L should have all the power you need to pull a 7000lb travel trailer. if you have the 4.8 it's still within spec for the truck, just a bit under powered. A good weight distributing hitch, and a sway bar should get you taken care of.

If your truck is having problems towing uphill a lower gear ratio rear differential will help. Adding a transmission cooler and a deep transmission pan will extend the transmission life. Make sure you have a good brake controller and trailer brakes. I would install load range E tires on your truck and if the tongue weight is too high use a weight distributing hitch and maybe overload springs on the rear.

This is a good solution if you have the budget for it, but if your truck is a 4x4 you have to change the front and the rear gears, which adds to the budget. If your truck is having problems towing uphill a lower gear ratio rear differential will help. Adding a transmission cooler and a deep transmission pan will extend the transmission life. Make sure you have a good brake controller and trailer brakes. I would install load range E tires on your truck and if the tongue weight is too high use a weight distributing hitch and maybe overload springs on the rear.

True - 4x4 requires front and rear diff gear changes.