[Joseph Smith]

I don't know if you can use the battery for a counterweight, but there's probably nothing specifically prohibiting it. IMHO, a Trebuchet is not the most practical way to hurl a two-foot ball. Trebuchets rely on the speed generated from the whipping action of the sling, which on a robot would probably exceed the 20" extension at some point.

However, if your heart is set on a Trebuchet thrower, I would recommend using a non-gravity powered method, such as using surgical tubing to pull the counterweight arm down. This allows you to save weight for other mechanisms.