Here's what I'd recommend:
Start with just enough weight to get the curds to stay together, for the whole wheel to hold its shape. You'll still notice cracks and holes/pockmarks between curds. (On many cheeses, including alpine, this tends to happen on its own, without any or much external pressure). Say, 15-30 minutes or so. Flip and redress the wheel.
Then up it a bit, until you lose more of indentations, the surface becoming smoother still. Another 15-30 minutes. Flip and redress again
Then at this point you can aim for a smooth surface, from higher pressure.
If, say, you wound up with a completely smooth wheel after just a short time during the first pressing, you probably pressed too hard and fast - this could trap whey in the cheese wheel, which down the road will ferment and make the cheese sour and weepy.
If you want mechanical openings in you cheese (irregularly shaped holes in the past when cut, often seen in Havarti for instance), then you would press just until you get that smooth surface, but not much more pressure than that. You would actually be leaving those gaps and spaces between the curd particles, though you wouldn't see any gaps on the outside of the wheel. (You want it smooth outside though, as holes and cracks give a place for mold to grow.)
If you don't want mechanical openings, the you press more, to press out those gaps between curd, making the curd uniformly compressed throughout the wheel. If you're aiming for a smooth paste of the cheese, OR aiming for round wholes from gas production (such as large eyes from proprionic bacteria in Emmental, or small eyes from diacetyl bacteria), you want those mechanical openings pressed out.
I find most cheese doesn't need a whole lot of pressure, not much more than 2x the weight of the cheese. It's the cheddar-types that need a helleva lot of pressure. So, if you have, say, a 4 pound alpine, you may not need more than 8 pounds of pressure/weight at the end of things. (So maybe step it up from start to finish from 2lbs to 4lbs to 8lbs for instance.)
A note about your spring-style press, though - since the cheese is pressed by the spring pushing against the top of the mold, as the cheese compresses (e.g. whey is pushed out; gaps are closed) and the the cheese shrinks in volume, the pressure actually lessens. So over time with the spring type press, LESS weight is applied to the cheese. So may have to be continually tweaking the screw for the first couple hours. Dead-weights, lever arms, and pneumatic presses by contrast apply a constant pressure over time.
