Welcome!!!
Concerning the manufactures "brochure" weights, the "dry" tongue/hitch weight does not include the weight of the propane tank(s) or a battery on the tongue. Those alone will add ~ 120lbs for 2-20lb tank and a battery, or ~ 160lbs for 2-30lb tanks and a battery, before even loading the trailer with clothes, food, bedding, or any other items (camp chairs, cooler, grill, etc).
What drivetrain does your '11 Chevy have, including the axle ratio?
You plan on having a second vehicle for all trips? Just you in the truck when towing the tt?
Also know that any accessories that you have added to your Chevy since you bought it reduce the trucks payload: truck topper/cap, tonneau cover, step bars, spray in bed liner, etc...
A good wdh with integrated sway control is always a good investment. The Reese Dual Cam, Reese SC, and the Equal-I-Zer 4 way system are all very good models for the money. The Reese hitch head (same for both models) does allow a little more fine tuning for the head tilt, but all three models are an excellent choice! The Dual Cam is a little more finicky to set up, and if you change the tw a fair amount it may need to be readjusted: if the fresh water tank is near the tongue, full vs empty which would affect the tw, you would need to readjust cams to the wd bars for the sway contro;l to work properly.
Good luck shopping!