Hang it from some part of the plane that WILL support it's weight, like the landing gear, or prop.
Gives you a close weight for the entire plane, but not so good for weighing a "chunk of balsa".
I have a scale that I bought at Staples for about $30 to $40. It's pretty accurate down to about 0.1 ounce, which may not be good enough for a small piece of balsa, but it will also weigh up to 12 to 15 pounds, so....
Dennis-