Have a V6 Toyota FJ Cruiser, tow limit is 5000#. Have towed a cargo trailer, Casita, Escape 17, Burro 13, and an Aliner Expedition. The Aliner was the easiest and best mileage to tow, the cargo trailer, though not the heaviest, gave me the worst mileage because of its non-aerodynamic shape.
The heaviest of all these trailers was probably in the low end of the 3k range. Have towed with and w/o sway bars and no problems either way, have towed over the Rockies and felt all but the Aliner. Have done this for more or less 10 years, part-time to full-time.
Having said that, I'm done with pulling trailers. They're too much of a hassle and limit where you can go (I like to go way out there). I'll tent camp and/or use a pickup and camper from now on, but YMMV.