A trebuchet looks something like this:
X
/|
L1- / | -L4
/ |
X O -M1
/|
L2- / |
/ | -L5
/ |
/ |
X---------------O -M2
|
L3
The X's are axis of rotation. The portion marked L1 is the portion of the throwing arm from the main axel to the counterweight basket. L2 is the portion of the throwing arm from the main axel to the sling. L3 is the sling itself, and L4 is the counterweight basket. L5 is the main support leg holding up the main axel. M1 is the counterweight, and M2 is the projectile.
In the trebuchet, the best designs call for a counterweight 100 times the weight of the projectile, L3=L2, L4=L1, L1*3.75=L2, and L5=0.707*L2