Circular force sensor: some basic questions about its functionality
With calibration you are trying to find out the "transfer function" of your system. There is an input and an output, and an unknown function of your sensor. So you vary the input (with the weights) and observe the change in the output. You can then chart this in excel or graphing software of your choice with an x vs y graph.

$$ Output = Sensor(Input)$$

The task at hand is to find out how the output is related to the input. If the system is linear and can be fitted to a first order polynomial you could use fit it with \$ y = m*x +b\$

$$ Output = m*(Input)+b$$

Or it might be a second order polynomial.

$$ Output = c_1*Input^2+c_0*Input+b$$

Once you find a good model for the systems behavior, the systems effects can be reversed and the observed output can be used to find out what the input of the sensor would be.

$$  Input= Sensor^{-1}(Output)$$

Another caveat to this is you may not be calibrating all of the inputs to the system. Temperature is often overlooked because it changes almost all sensors. So you may calibrate the system at one temperature only to find later and find a different result at a different temperature. The difference in accuracy may or may not be critical to your application.