The spring or coil is the actual physical resistance to lowering the ride height. When you bounce the truck, the shock is what should be stopping the bounce with maybe one rebound. The shock will also slow the compression of the coil with it's hydraulic force, but if you load weight and leave it in, the shock is not affecting the final resting place of the ride height.
I just checked mine on the way to the mailbox. I pushed down with all of my 220 pounds on the ball of the tow package, which should give me a good bit of leverage. The truck went down maybe an inch, maybe less. When I jumped off, it rebounded up and stopped moving.
I then "unloaded" about 150 pounds (maybe more with the leverage) by lifting on the trailer hitch. The truck lifted about an inch. So, theoretically, I should be able to drop the truck almost 2 inches if I first unloaded some weight (the spare tire, the tonneau cover, and all the tools in my bed compartments might lose it 100 pounds or so.)
If you have 3 inches of drop, either you've got worn out coils, you've lost a few hundred pounds of weight from the back, or both. Also, since you have 3 rebounds, you've got bad shocks.