I have been there. The Trailblazer was a great vehicle and it did a fair job towing my 2005 Jayco 21J. However in heavy winds it was a handful to control! If you have the extended version with the 5.3L I think it might be a pretty decent tow vehicle. I had the short wheelbase and 6cyl engine.
I had the opportunity to pull my 21J with an extended cab Dodge Diesel. I did not even know it was back there.
I did change to a Chevy Avalanche, which made all the difference in the world. With the Avalanche we pulled that little 21J all over the country and loved it!
For me I like a longer wheel base vehicle, they don't rock forwards & back and the longer wheel base helps with sway! I know pull a 26" trailer with a 2015 Chevy Silverado 1/2 ton Crew Cab. Perfect for a 6000 lbs trailer!
Happy Camping & travel safe!