One of the key design improvements that medieval engineers made in the trebuchet was in the design of its counterweight.
Even the earliest military technicians understood the potential of "the seesaw effect" of a lever. As gravity pulls a heavier weight down on one side of the seesaw, the lighter weight on the other side of the seesaw's fulcrum is lifted. If the object on one side falls with great force, the one on the other side might become airborne.
When military designers tweaked the point of the axle on the lever arm (creating one arm longer than the other) and raised the axle high above the ground, they had built their first functioning trebuchet.
But how did these military men maximize the downward pull of the short arm? The answer: They added literally tons of weight. During the siege against the Scots castle of Stirling, Edward I of England sent orders out to strip all of the church roofs in the entire surrounding area of lead. These gathered sheets of lead were believed to have been melted down and then attached to the counterweight of the trebuchet. The lead attached to the NOVA-built, fixed-weight trebuchet weighed a hefty six-and-one-half tons.
The most efficient way for any counterweight to respond to the force of gravity is by falling in a straight line. It's the same reason that a free-falling stone dropped from an altitude of 3,000 feet will hit the ground with greater force than a rock that is rolled down the side of a 3,000-foot mountain. In a fixed-weight trebuchet, the weight must fall in an arc, following the arc at the end of the lever arm.
The hinged counterweight, however, is free to follow a straighter descent to the ground, providing the trebuchet—and eventually the launched stone ball—with an even more devastating power.