Could everybody, PLEASE, just do this test for yourself and stop making guesses which is just confusing the OP and anyone else trying to learn this principle.

Stand in the middle of the room. Bend down and pretend that your on a road bike in the drops in a tucked position. Was it hard to do? No it was dead easy and you have NO weight on your hands at all so how did you do it so easily?
Look where your backside is. Its WAY out behind you balancing your weight over your feet.

Now, back up to a wall and try to lean forwards into a crouch. You fall forwards. Why? Because you can't move any weight backwards to balance yourself.

On a bicycle the Crankset/Bottom bracket is the centre of balance of the bike. Moving the saddle backwards moves your centre of gravity back a little behind the BB placing less weight on your hands/shoulders. Moving the saddle forwards moves your centre of gravity forwards placing more weight on your hands/shoulders.

Aerodynamics, power, stretching out are all red herrings in this matter.