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Two additional thoughts on that (assuming you're talking about a balance of sorts, since that seems like the easiest thing to make ghetto-style): First, make sure to test / calibrate it by checking that you can weigh some number of nickels against twice as many pennies and measure them as equal to be sure that it doesn't mechanically favor one side. Second, keep in mind if you hadn't already thought of this that you could weigh more precise measurements by adding coins to both sides, ie a nickel on one side and a quarter on the other would only be adding about 2/3 gram difference to the quarter side. I wouldn't trust it to be perfect, but you could probably figure something that'd be reasonably accurate to some fraction of a gram.
Cool idea, post back if it you actually get this working. I'm curious.