What’s the most a 07 Trailblazer 5.3 AWD can tow/stop safely

What is the GVWR of the trailer? In most states if it is 3000lbs GVWR or higher you need brakes. In some states the limit is 1000lbs GVWR. Depending on the state it may be only on one axle, but many states require brakes on both axles.

The cops may have issues with the lack of trailer brakes if you do get pulled over for a moving violation. Not always, but there is the chance.