I have a 16 foot dual axel flatbed trailer that I tow with a ram 3/4 ton. It's rated for 7500 lbs, is a bumper pull, no sway bars. I've had it very heavy and it tows just fine. If your suburban suspension is up to the tongue weight you should be ok without sway bars though I've heard they are beneficial. Important is to make sure the traileer is level (ie not so tongue heavy that the front of the trailer inclines, you get excessive sway in that condition.) Longer trailers will also tow better than shorter ones. Not really sure why though.........