The way I think about it is that the two tires and the hitch are the only parts of a trailer that "ground" it. These three points (the tires and the hitch) make a triangle. The whole contraption is most stable when the center of gravity is within this triangle.
One way to visualize it is to think about a square shovel sitting on the ground facing up (so that if you step on the cutting edge the handle could flip up and hit you.) Similar to a trailer, the points of contact make a triangle -- the handle, and the edge of the shovel on the ground. Now stand on the shovel anywhere inside that triangle and try to "steer" it by twisting your foot... not going anywhere. Now stand on the cutting edge (outside the triangle) and try to "steer" it -- really easy, right?
Now have a friend hold up the handle of the shovel while you do the same thing. As long as the friend can hold up your weight, they'll have a relatively easy time "steering" the shovel no matter where along the handle you stand, and you won't have much luck "steering" them. Of course if you load too close to the handle your friend will drop you, and the closer you get the more effort it will take to move the handle the same distance, because they're moving YOU farther and farther with every inch you get closer to them. Friend still holding the shovel handle, stand on the cutting edge. Now they have to press down on the handle (instead of holding up) and they'll have to fight you if you try to "steer".
Back to trailers and you add a few more dynamics. Too heavy a tongue weight can damage your tow vehicle's suspension as well as taking weight off the steering wheels, making steering light. Some tongue weight provides the stability of the weight staying inside the triangle without the disadvantages of too heavy a tongue weight. Finally, too light or negative tongue weight means you're standing on the cutting edge of the shovel, and the weight on the back of the trailer will try to steer the tongue every chance it gets. If the tow vehicle is lighter than the load, the load will steer the tow vehicle. If the tow vehicle is heavy enough to avoid being pushed, the "steering" effort doesn't just go away... it gets transferred to anything that will move -- the play in the hitch or pliability of the tires, causing the trailer to sway back and forth.
I could be wrong but that's how I think about it...