This Trailering Guide (PDF) from Chevrolet explains that a Silverado 1500 can tow a trailer with a maximum weight of 13,300 pounds. It does not seem to differentiate between engine sizes (click on the "view full guide" button):
Utilize this guide to help find the right Chevy Truck for your trailering and towing needs, and learn more about trailering basics, like curb weight and more.
www.chevrolet.com
For a given individual truck, there is a Label inside the driver's door that is more specific.
... and then on page 28 of the brochure pdf, it says that a Trail Boss with 6.2L can tow 9,300 lbs.