I didn't want to hijack his thread but since you sort of ask here, I'll explain that part.

By hanging your legs down loosely and feeling for yourself how much weight your hands are holding, you'll realize that all of the difference from moving the seat back is from support of the muscles around your midsection. Almost none of it is from balance, or from the physical mechanics of leverage. I say "almost" because a small bit (like 2 or 3 percent) shifts due to the longer lever arm if you move back and straighten your arms. But that's an insignificant amount compared to the weight you feel on your hands.

The legs hanging down remove them from the equation, so that you can understand the balance of the torso, between the seat and the bars. The only time that's not relevant is if you're hovering over the seat. All of that weight that you'll feel has to be taken up by your core, after you brace your feet on the pedals.

So moving the seat back does not mechanically change the weight on your hands. You have to brace your feet for that, and for that reason the real effect of moving the seat back is in changing the angle of the hips and lower back. It is physiological, not physics. Certain angles may make it easier to hold your torso up, but it's not because of a change in the actual weight balance. You're changing how the muscles react, using reach and torso angles.

It makes a difference, because what if the rider says that moving the seat back didn't help? You think it has to, because it's a mechanical law (tho it's not) that there's less weight on his hands. Then what, move it back more? In reality, perhaps it didn't help him because he doesn't have the core strength to hold up at the aggressive angle. He needs to sit at a higher angle. Or maybe his back is bowed and he fatigues, and a longer reach would help him. You can't get to that by using a faulty physics formula.