It's possible to define "weight transfer" in very few words, understandable by the average dragracer:
Weight transfer is the increase in vertical loading of the rear wheels that occurs during launch.
But, this definition doesn't begin to answer many of the questions that arise when dragracers start benchracing.
For a very basic starter: What causes it?
To adequately answer that apparently simple question, we have to go back to a time when there were no dragstrips. There weren't even any cars. There was, however, a very bright young man by the name of Isaac Newton. The popular story is that he was lying under an apple tree, in about the middle of the 17th century, when an apple fell from the tree and hit him on the head. Now, the only idea I would have gotten would have been to gather more apples for a pie, but young Isaac was prompted, instead, to develop his Laws of Motion. While the apple story is most likely a fable, the incident would have demonstrated one of his maxims: The force on an object is equal to a change in momentum of the object. But, we need to put that in other terms before applying it to dragracing.
Long before Isaac and his apple came along, engineers had a pretty good understanding of the forces encountered in a structure and in the use of a lever. But, it wasn't until about a hundred years after Isaac Newton that another man demonstrated that these ancient principles could, with a simple "tweak," be used with Newton's Laws of Motion. His name was d'Alembert and that which is known as "d'Alembert's Principle" is the idea that problems involving the acceleration of bodies can be reduced to relatively simple static problems with the application of a little imagination; specifically, the application of an imaginary force.
Suppose, for instance, that a force is accelerating a block of material. Instead of considering the block in motion, we can consider it to be stationary and that the accelerating force is acting against an equal and opposite force, acting through the block's CG (center of gravity). Another way of expressing this force is to say that, according to Newton's Laws, its magnitude is proportional to the product of the block's mass and its acceleration. This force doesn't actually exist, so we must consider it "imaginary," yet, to a dragracer, the concept should be so evident that it's difficult to consider it as anything but real. This force is called the "inertial" force.
It's important to realize that this added force is ALWAYS in a direction opposite to the direction of the acceleration. In the normal dragstrip situation, the rear tires are exerting a force in the direction of the acceleration. Using d'Alembert's Principle, the reaction is a force, acting through the CG, in exactly the opposite direction.
The forces are equal, but in opposite directions. This is one of those principles developed by those ancient engineers: Forces must be "balanced" on a body at rest. That is, if you consider an arbitrary direction for a body at rest, the external forces acting in one sense (of that direction) must be equal to those acting in the other sense. For instance, the sum of the four wheel loads must equal the weight (gravitational attraction) of the car.
Another ancient principle is that the sum of moments about any arbitrary axis of rotation must be zero. To illustrate this, we might as well go directly to the car during launch.
We've already established that the forward thrust of the rear tires is equal and opposite to the inertial force. But, the tire thrust force is at the strip surface level while the inertial force is acting through a point some distance up from the strip surface. Two equal, opposite, and parallel forces, acting at different locations (in this case, at a spacing equal to the height of the center of gravity), constitute a "couple" or "moment," the magnitude of which is the product of one of the forces and the spacing. If we select, as an axis of rotation, a line through the front tire patches, that line would appear as a point in the side view. Consider the car in the illustration. The situation described would provide a CCW (counter clockwise) moment. But, it's been stated that the ancients established that the sum of moments, about any point, must be zero. So, we must somehow find a CW moment of the same magnitude. And, this is where the "weight transfer" comes in.
If equal and opposite vertical forces are acting at the front and rear tire patches, we have a second couple with a spacing equal to the wheelbase. So, if the magnitude of this couple equals that of the couple just described and if we associate a negative value with CW (clockwise) couples, a sum of the two couples results in the desired value of zero.
Again, looking at the illustration, we see a force acting upward at the rear tire patch. (This is, of course, actually two forces acting at the two rear tire patches.) You should immediately recognize this as that which we call the "weight transfer." The force at the front tire patch is in the opposite direction, which might seem puzzling, as it would appear the the front of the car is being pulled down. This is because, when we think of vertical forces, we tend to think of the force that the car exerts and not the force being exerted on the car. At the front, the couple force is down, but the force exerted by the strip surface is up as it supports the weight of the front end of the car. So, that downward couple force is going to simply subtract from the static upward force. At the rear, the forces will be additive.
But, what if the front end of the car weighs less than the couple force? Not to worry! We simply add another imaginary inertial force...a vertical one this time...at the CG to maintain the couple balance. This represents what will eventually be a "blowever" unless the forces change in a manner that halts the upward acceleration of the car.
Note that, in determining the value of the weight transfer, no consideration is given to the "internal" workings of the suspension. Suspension design parameters affect weight transfer only when they affect CG height and tractive force.
An example of the former would be the use of low rate front springs. An example of the latter would be any effort to equalize rear tire loading for maximum tire effectiveness.