When the projectile is loaded into the sling of the trebuchet and resting on the projectile runway, the counterweight is fully raised. This would represent 100% gravitational potential energy, so a pie chart showing the divisions of potential energy versus kinetic energy (energy of motion) would be 100% PE/ 0% KE.
Upon release, the potential energy stored in the counterweight accelerates down towards the Earth. This starts a transfer in energy from 100% potential towards production of motion, starting from 0%. A pie chart showing this transfer of energy might be shown at the half-way point of the counterweight's descent, such as 50% PE/ 50% KE.
When the counterweight is at the bottom of it's swing, the potential energy has been exhausted, and is at 0%, while the energy it had stored has all been transferred to kinetic energy, 100%. A pie chart of this would show 0% PE/100% KE.
The counterweight will continue to move in an upwards fashion, against the force of gravity,again building potential energy for another swing. The energy stored into this swing will not be as much as the initial swing, however, due to some of it being transferred to sound, friction, and heat. Another pie chart could represent this as 100% PE/ 0% KE.
The counterweight will again start it's descent, transferring the potential energy stored into kinetic energy. At the bottom of the swing, another piechart would show the potential energy to have all been converted into kinetic energy: 0% PE/ 100% KE.
Ultimately, all the stored energy, 100%, will be transferred into one form of energy or the other, until the counterweight and the throwing beam remain motionless in an upright, vertical posititon.