Indeed. But by just specifying a weight, you aren't really controlling the process as different sized cheeses will end up with different pressing forces, so will come out drier or wetter than intended. By specifying pressure you can maintain a parameter which ultimately will lead to better cheese as you experiment.
My general approximation of 50psi tends to work pretty well for harder cheese styles. Think a real farmhouse cheddar consistency more than brie. Its a good compromise between getting plenty of water out and not running it off so fast that the cheese goes chalky from being dried too fast.
If you want a harder cheese, press longer rather than harder. If you want to press a softer cheese, press shorter first, then experiment with less pressure. If you don't press hard enough you won't expel enough water and it won't set up properly (OTOH you might find you quite like a cheese which is hard on the outside and softer in the middle.
Also worth noting that you should turn the cheese in the press every day for the first few days, this stops it drying more at the top than the bottom.