Set the spring gun to the desired spring compression position.  There are three different positions to chose from.   Observe that different mass balls will go to different heights at the same spring compression setting.  We usually use the 2nd notch of compression for this demo.

The cup in the spring gun that the ball sits in has a mass of 56.5 g that must be added to the mass of the ball when doing the situation where a ball of half the mass will go twice as high.  So for that situation we have two balls that are to be used which have masses of 15 g and 86.6 g.  Adding in the mass of the cup gives you:  56.5 g + 15 g = 71.5 g, and 56.5 g + 86.6 = 143 g, or a 1:2 mass ratio that the spring is pushing.