I don't know if I can adequately explain the principle of a weight distribution system in just words (ya know what they say about a pic being equal to 1,000 words). But I will give it a try.
The principle behind all (as far as I know) weight distribution systems is to, using the spring bars, transfer some of the felt tongue weight on the rear of the tow vehicle to the front wheels. As I said in my earlier post, most weight distribution systems are incorporated into a specifically modified ball mount, and using the spring bars, which are locked into the ball mount, they impart a rotational torque to the tow vehicle through the hitch mounted on the vehicle. When towing without a weight distribution system, all the tongue weight generated by the towed vehicle is directly applied to the ball mount through the ball coupler on the trailer. Since the ball mount is behind the tow vehicle's rear axle, this tongue weight causes the front end of the tow vehicle to lift because the rear axle of the tow vehicle acts like a fulcrum point of a lever system. The heavier the tongue weight, the lower the rear suspension squats and the higher the front of the tow vehicle lifts. and, there is a vertical pivot point where the trailer coupler meets the ball on the ball mount. What the weight distribution system does is, in essence, stiffen the pivot point at the coupler/ball mount, using the spring bars which are anchored at one end in the ball mount, and tied to the trailer frame behind the coupler using either support chains or support brackets.
There are two main adjustments that are made to a weight distribution system to achieve the desired amount of weight transfer. One is the amount of spring bar tension, made by adjusting the length of the chains or support bracket, and the other is adjusting the angle of the ball mount in relation to the tow vehicles hitch. If the system is adjusted properly, before the chains are connected to the spring bars, when the coupler is attached to the ball mount, the tongue weight will cause the spring bars to angle down, away from the trailer frame. Tension is put on the spring bars when you attach the chains or support brackets, and this tension is transmitted through the ball mount because the bars are fixed to it. Because the ball mount is fixed to the vehicle hitch, this tension is transmitted to the hitch. The hitch then transfers this tension to the tow vehicle through its mounting points. This is the hard part for many to understand, unless you envision the entire system from the side view. This rotational force causes the rear of the tow vehicle to lift slightly, and the frame forces the front of the tow vehicle down, which effects the weight transfer to the front axle. Now, the hitch that is designed to work with a weight distribution system, is rigidly mounted to the vehicle frame, and doesn't allow any twist between the mounting points and the receiver socket, so any rotational force is directly applied to the vehicle frame. With the V6 crossmember type receiver, the crossmember isn't as rigid as the other type of frame mounted receiver, and if enough rotational force is applied, it will twist while trying to transfer this torque to the frame. With a fairly light trailer, and low tension applied to the spring bars, the rear crossmember may be able to handle the load. But as the spring bar tension goes up, with heavier trailers, it will twist.
If this attempt at an explaination doesn't answer your questions, or make sense to you, I suggest you visit one of the weight distribution system manufacturers sites. I use an Equalizer system, and their site has a very through FAQ section which may be of more help. They use pics to illustrate the theory of weight distribution, which may be of more help.