Alpkaserei--have you seen this in both horizontal presses and vertical presses or just vertical presses? I don't mind my analysis being incomplete--and it clearly is if reality doesn't behave the way my analysis describes it should (or I could have just made a mistake...).
I don't like the train example because the delay in the force reaching the last car is due to the distance required to travel before engaging each successive car. When pressing a stack of cheeses (I assume, because I've never used a horizontal press) the cheeses are not left with any distance between (and, I suppose, if they were, the time required to engage all of the cheeses wouldn't count in the pressing time).
A better model, perhaps, is that of a spring and damper. Most people are familiar with a spring (though they often have misconceptions about how they work...). A damper is usually described as a piston, with holes in it, held within a sealed cylinder that is filled with some fluid. When the piston is pushed, it travels through the cylinder, forcing the fluid to travel through the holes in the piston from one side of the cylinder to the other side. Many automobile shocks contain dampeners and they are often found on doors to prevent them from slamming shut. If the holes are large and the fluid has low viscosity (it's runny) then you can apply a great deal of force to the piston, and only supply a small deal of force in the opposite direction to the cylinder to prevent the cylinder from moving. If the viscosity is high and the holes are small, most of the force that is applied to the piston will need to be applied to the cylinder in the opposite direction to prevent the cylinder from moving. In both cases, the piston moves. Regardless of the size of the dampening coefficient (how much damping the damper does), once the piston has reached the end of its travel, all force applied to the piston is transmitted directly to the cylinder.
If we go back to the cheese now, we can model it as a spring-damper system in series--that is, the cheese press pushes on the damper of the first cheese, which then pushes on the spring of the first cheese, which pushes on the damper of the second cheese, which pushes on the spring of the second cheese, etc. If you imagined having a uniform mixture of curds and whey where the ratio of whey to curds was sufficient to prevent the curds from touching each other, this model would be pretty good. Instead of the classical dampener, we've left the piston (the follower) hole-free, and filled the cylinder (the mold) with holes. As we press on the "cheese" the whey leaves the cylinder, damping the force of the piston. In this case, we'd expect to see a lot of whey coming from the first few cheeses and very little, if any, coming from the last few for the first while of pressing. In this model practically all of the whey would be pressed out before the curd started to knit (because the springs, the curd, wouldn't have to carry much load until all the dampers were completely bottomed out).
A better model, in my estimation, is that of a spring-damper system in parallel--that is, the press pushes on both the damper and the spring of the first cheese at the same time. These two from the first cheese, then push on the spring and damper of the second cheese, and so forth. In this model we can think of the curds as the spring and the whey in the mold as the damper. When a force is applied by the press, a portion of it is supported by the spring--this portion of the force is transmitted directly to the next cheese (and through all of the cheeses). The remaining portion of the force is carried by the damper. How large this portion is and how much of it is transmitted to the next cheese depends on the characteristics of the damper. If the spring is really weak, and the damper has a low damping coefficient (lots of holes and a non-viscous fluid), then we'd expect to see a similar phenomenon as we saw in the previous case--a lot of whey coming from the first few cheeses and very little (though a bit more) from the last few. If the springs were not weak, and the damping coefficient high, we'd expect to see a more uniform loss of whey, though the first cheeses would still lose a little more than the last.
What might be the most accurate model would be to combine these two models. The whey can be modeled as a damper, but the curd itself, if drained well, for example, is probably well modeled as a spring-damper system (though it probably is more like one in parallel than in series). In this case, the whey has one damping coefficient (probably relatively small) and the curd's damper has a different damping coefficient (probably a lot higher). If I recall correctly, you can combine the two dampers into an "effective" damper and you end up with a model like the second model, where the damping coefficient is somewhere in between that of the curd's and that of the whey's.
The relative intensity of pressure (or the force) experienced by the last cheese, when compared to the first cheese, depends on the stiffness of the spring (or the stiffness of the curd) and the damping coefficient of the whey/curd damper. If the curd is very stiff, regardless of the damping coefficient, the difference in pressure experienced will be small, if the damping coefficient is large, regardless of the stiffness of the spring, the difference in pressure will also be small, however if the curd is not stiff and the damping coefficient is small, the difference will be large. Of course, if things are more moderate, the difference will, too, be moderate.
Now, how to measure the damping coefficient and stiffness of cheese during pressing.
And despite writing all of this boring stuff at 0200 in the morning, I still don't know if I can go to sleep. Curse this dumb cold...