So for the weight sensor I put 10 volts across the green and black and then measure the voltage difference across the white and red by plugging it into the microcontroller ports?
Yes, but not directly to a micro-controller's analog (ADC) inputs.
First, I would be leery of getting 10V into the micro-controller pin which will destroy the micro-controller. So use 5V (assuming a 5V micro-controller) so this is always safe. Later you may use 10V excitation but ensure you have protection on the micro-controller pins.
Second, With the micro-controller's ground connect to the load cell's power ground (black wire) you can connect the two outputs (white/red wires) to two ADC inputs on the micro-controller. Read the ADC values then take the difference in software will give you the load cell differential output Voltage which is proportional to the load on the cell.
Third, the differential Voltage (white/red wires) is probably going to be fairly small (I could not find in the DS what the differential Voltage per kg is). The differential Voltage does increase with an increased load on the Cell. If the
Full Scale (max weight on cell) differential Voltage output is small compared to the ADC reference Voltage then you will need to amplify the differential Voltage with some op-amps.
Once you add
op-amps then its best to use a differential op-amp or
instrument amp configuration to produce a
single ended output Voltage. Then you only need one ADC input on the micro-controller.
The first step is connect a Voltmeter to the Cells outputs and apply power. Then measure the differential Voltage output while increasing the load on the Cell. This will tell you whay Voltage values you are dealing with and then you can go and design the circuits and/or ADC code.
Post back here your results from this testing for more help. BUT, do some more google searching on the terminology I just used (bolded text).