Physics Application: Force

Modifications that could be made to increase range:

Release Angle of the sling: The release point of the sling is the most crucial part of the trebuchet. Release too low and your balloon goes backwards or straight up. Release too high and your balloon goes straight down with not only the force of the counterweight, but gravity added at the last second. Therefor releasing the catapult at the perfect angle gives a balance of distance and height causing it to go as far as possible.

Weight of counterweight: This is pretty simple. The more weight you have, the farther the balloon will go. But, too much weight and your catapult will either break under the pressure, or the whole thing will be unbalanced and toppled over. At the same time, if you don't have enough weight, you wont have enough force to not only move the weight of the arm, but the sling as well. So, you must have a decent amount of weight to move the arm and the sling, but also move it fast enough to get velocity out of the balloon.

Height of the swinging arm: Due to restrictions you cant make the height more than 5 feet. But if restrictions were abolished essentially the longer the arm, the more centripetal force would be acted on the arm and especially the swing, causing a larger velocity. Rather than a short arm only being able to move a short distance, a longer arm would create a longer distance to travel causing a greater buildup of velocity at release. But then again too much length of an arm and the arm could break under the pressure of the weight unless the arm was really sturdy and thick, preferably the trunk of a tree.