I just tore apart my scale for the heck of it and it's very similar to yours inside. It has the same black, red, green, and white wires coming from the sensor itself. After some messing around I came up with this schematic (see image) where the two potentiometers are the flex sensors used to measure the weight (one is compressed and the other is stretched). If you measure the voltage between the green or white wire and ground you will see that it changes a little bit when you weigh down the scale. You can hook up these wire to analog pins on the arduino and with a bit of software and calibration you should be able to get the weight.
