Ignoring basic overload breakage possibilities...
Have you weighed your combination? Compared the rear axle weight with your vehicle's rear axle gross weight rating?
Having done just this myself and found myself a couple hundred over I find your question very interesting.
A spring will bounce or oscillate at a certain "natural" frequency. As you increase the weight on a spring that natural frequency becomes lower. This is how you get cushy Cadillac suspension. Ever notice how differently your truck rides empty compared to loaded? Empty is jiggly which corresponds to a high natural frequency and loaded is floaty/bouncy which corresponds to a low natural frequency.
So the first step is to increase the spring rate(s) to handle the increased weight and get the natural frequency back up. For leaf springs this could be as simple as adding a leaf. For coil springs it might mean having custom springs wound or finding an interchangable spring with a higher rate.
Once you increase the spring rate you will also need to increase the damping of the shocks to match. Again off the shelf will not work and you are looking for something outside the box. There are shops which can custom calibrate shocks or help you obtain custom calibration.
These options may not be cheap... until you compare them with the cost of a new truck