There are so many factors that go into the final taste and texture of cheese. Of these, at least for my own cheesemaking, pH at the point of salting is one of the most significant. Not the only one, by any means, but definitely the single most important variable that I have control over that makes the biggest difference. Next most important is probably the final moisture level of the curd.
However, I would say that pressing protocol is not the best way to control the overall moisture in the cheese, except to be sure that you are not trapping whey in the cheese by pressing too much too soon. Take this with a grain of salt, since I am no pro, but my sense is that final moisture is far more dependent on length of set (or, flocc multiplier used) and how the curds are treated - size of cut, amount of stirring, time and temperature in cooking, even to some extent cheddaring, milling, and salting. If these factors are off, giving you curds that are too wet, I don't think you can successfully adjust the moisture level by press weight. (And I'm VERY sure that if you wind up with curds too dry, you can't correct by pressing, no matter how much weight you add! As the old woodworking joke goes, "I've cut this board 3 times and it is STILL too short!")
Again, I'm no pro - maybe Sailor or someone else can chime in to correct any mis-statements above!