Reg is right about the dynamics at work in a rear-loaded trailer. In airplanes tail-wheel airplanes are notorious for "ground-looping," where the aircraft rotates around the main landing gear in a spinning fashion. The center of gravity is behind the wheels, and wants to be in front, where the tires are being drug, rather than pushed. Darts are similar, too: if you throw one backwards, the heavy tip will rotate so it leads the resistance of the fins.
If you drive your car backward and steer, the center of gravity follows the steering tires and tends to exaggerate the movement, and will make it keep steering more in that direction. It's a positive feedback cycle, and is why rear-steering things are so squirrely.
The trailer wobbles when loaded to the rear for the same reasons. The center of gravity is behind the resistance of the tires, and has a pivot point at the hitch. It goes sideways, then force builds up in the springs, tires, and frame. If the tires don't skid, eventually those forces will bounce the trailer back the other direction, and the cycle starts over again.
This also explains why accelerating can sometimes stop the wobble, and braking usually makes it worse. Under acceleration the center of gravity will tend to be in line with the direction of pull, or straight. Under braking, the the center of gravity tries really hard to get in front of the resistance to its momentum.
That's oversimplified, but close enough to the principles at work.