It sounds like you don't have the weight-distribution part of the hitch installed (or perhaps just not properly set up.) Here's a link
to Equal-i-zer setup instructions, if you don't have them. With a weight-distribution setup properly installed and configured, the front and rear bumper of the truck should drop by approximately the same amount when the trailer is on the ball and the weight distribution hardware is set.
Your shocks have nothing to do with how far the truck drops when you apply weight to the suspension, they control how fast it drops (and/or rebounds). Your springs have little to do with it unweighting the front while compressing the back, they'll respond correctly when the weight distribution is set correctly.