Lever question rotation torque

If I have a lever and fulcrum and I am applying 1 pound of pressure 12 inches from fulcrum on one side to lift a 2 pound stone 6" from fulcrum on the other side. Question is why does the fulcrum have a total force of the 3 pounds (plus lever weight) when applying the force at 12" ,but when I try to emulate the force at the 6" point on the side I am applying the pressure I have to apply 2 pounds of force making 4 pounds of downward pressure on the fulcrum. The farther I move my hand away from fulcrum less total pressure on fulcrum but same rotational force. SO my question is if I cut the lever at 6" why can't I emulate exactly the physical motions that are causing the rotational force with only the 1 pound of force downward weight on fulcrum? How is that rotational force being generated on the molecules of the lever at 6" from fulcrum that allow me to lift a 2 pound object with 1 pound but when I cut the lever substrate and try to emulate this same force I wind up applying 2 pounds to now lift the 2 pound weight the same distant on the other side. Basically how is it possible to get more rotational force and less downward weight force on the fulcrum the farther I move from it. The closer I am to fulcrum the more total weight down on fulcrum to get the same rotational force. What exactly is happening and why is it if I cut the lever I can't emulate what is happening to the molecules in the lever to not apply the downward weight on the fulcrum but still apply the same rotational force which seems to be what happens the farther you move away from the fulcrum the more rotational force(torque) and less force downward on fulcrum. I tried this with my finger as fulcrum and it is true everything I said but I can't figure out what exactly is causing the more downward weight force on the fulcrum with same rotational force.

• -1. This question is a wall of text. It requires some editing to make it easier to read. – sammy gerbil Oct 17 '17 at 8:01

You can think of it by an easy physical principle: Work $\Delta W=\int \vec{F}\cdot\mathrm{d}\vec{r}$.
So if you want to rotate the lever by a certain degree $\varphi_0$ around a point $\vec{r_0}$, you will get the same amount of work $\Delta W$ on both sides (can be proven easily).
This means: $\vec{F_1}\cdot\vec{r_1}=\vec{F_2}\cdot\vec{r_2}\quad$, where $\vec{r_1}, \vec{r_2}$ are the vectors from the rotational centre to the point where the forces are applied. So this effect relies on the equivalency of the $\Delta W$'s on both sides.
The principle of work itself relies on the axiom of force $\vec{F}=\frac{\mathrm{d}\vec{p}}{\mathrm{d}t}$, which can't be proven mathematically, but is one the best tested principles.