Very simple. With a given torso position, everyone has a certain center of gravity. If you have 45% of the weight on the front and 55% on the rear you know that the center of gravity is located a distance of 45% of the wheelbase, from the rear of the bike.

If you move the saddle back 1cm it will roughly reduce the weight on the front by about 1% and increase the weight on the back by 1%, since the wheelbase of the bike is not greatly less than 100cm. This is easily proven by placing a scale under the front wheel, with the rear wheel blocked up so the bike is horizontal. You can also prove that lowering the torso adds a lot of weight to the front wheel, compared to riding in an upright position.

If you move your nads forward, as you would with a longer stem, there is little change to the weight balance.