Desperate times sometimes call for desperate measures. I wouldn't consider towing more than 1000lbs with my Aveo unless I had absolutely no other options. I'd be comfortable towing 800lbs, but towing a trailer approaching a gvw of 2000lbs would be foolish IMO. I have also worked at U-Haul (about 10 years ago) and can say they will never touch one of my vehicles.
You may want to look at the little trailers at Tractor Supply. The price might be about the same as the Uhaul rental and the trailer would be a bunch lighter...but it would also be open and reqire you to tarp the load.
Disclaimer: I have not towed with my Aveo yet. I have towed several different utility trailers with small cars.