LEGO balance

You can make a sensitive balance using LEGO. The only non LEGO parts are three small round steel rods used as the pivots. I used from an old DVD drive mechanism, but you can substitute smooth nails, etc. The key is to get the center of gravity for the balance beam just right, if too high, it will tip to one side and stay, if too low it will not be sensitive. You can stack additional LEGO's over the center pivot point to adjust center of gravity.

See: http://sci-toys.com/scitoys/scitoys/mathematics/microgram_balance/balance.html for tips on how to create standard weights to use and how to calibrate your scale.

An additional improvement is to attach a small reflective mirror to the side of a LEGO brick at the fulcrum point and mount a laser pointer so that the beam is reflected on a surface with a ruled strip of paper attached. This optical lever will greatly magnify the sensitivity of your device. You should be able to measure to less than .001 gram.