Something has always got to be pushing back. If I put 10 lbs of load on one side of something, if it's in equilibrium (not moving), then something is pushing back with 10 lbs.
In a vertical cheese press system, the load carried by the bottom cheese (assuming no load is transfer to the molds--which a good design would try to ensure) would be equal to the load applied to the top cheese plus the weight of each of the cheeses and molds on top.
In a horizontal system, you can introduce a little bit of complexity in the analysis if the molds are resting on something, but if they are suspended between the load applying end (a piston of some sort, perhaps) and the "base" such that those are the only two points in contact with the stack of cheeses, each cheese will experience the same force.
So, in the case of an infinitely long, horizontal stack of molds, if the molds are only touching one another, they will each be carrying the same load. If they are resting on the ground, the friction between each mold and the ground will lessen the load the next cheese carries until there is no longer any load applied to the cheeses. Example: 10 lbs of load is applied, cheese 1 experiences 10 lbs, but 1 lb of the reaction is provided not by the next cheese in line, but by friction with the ground. Cheese 2 expereiences 9 lbs, Cheese 3 8 lbs, etc.