Electronic – µC control of a force testing machine

If you have huge transient error spikes, then you need a derivative part (i.e the D in PID) to handle these.

A simple PID system is not hard to write in code, it's the tuning that's the difficult part - you need to know roughly. The integral part will handle the DC offset, the proportional part the gain, and the derivative the reaction to change.

Here's some code I wrote for a temperature controlled etching tank I made with a PIC16F and a DS18B20 temp sensor ages ago (it used some nichrome wire driven via PWM wrapped round a couple of ceramic tiles for the heating element, so it had a large thermal capacity)
The results, once tuned, were an overshoot a of less than 2 degrees on power up, and a variation of less than a degree or so thereafter. It's very old code for a one off project thrown together quickly, so it can probably be improved a fair bit.
I found this document "PID without a PHD" quite helpful. Also, Matlab, Scilab or Octave can be used to simulate and tune PID systems.

/** Control variables **/

int DEADBAND = 0;   // Range where no change will be made

// PID gain values 
double Kp = 10;
double Ki = 0.02;
double Kd = 5;

// Accumulator variable for Integral calculation
double I_acc = 0;

// Returns out the proportional term
double get_prop(int error)
{
    double p;
    p = (Kp * error); 
    return p;
}

// Returns the integral term
double get_int(int error)
{
    double i;
    I_acc += (error);

    i = (double)(Ki * I_acc);
    if(i > 1000) i = 1000;
    if(i < 0) i = 0;
    return i;
}

// Returns the derivative term
double get_deriv(int error)
{
    double d;
    static int prev_error;
    d = (Kd * (error - prev_error));
    prev_error = error;
    return d;
}

double get_pid(int error)
{
    double result;
    double p, i, d;

    p = get_prop(error);
    i = get_int(error);
    d = get_deriv(error);
    result = p + i + d;
    return result;
}

Digital scales with range 10g and claimed resolution 1mg are available for low cost. There's no reason why you couldn't remove the load cells and substitute your own circuitry. The resolution is not necessarily an indication of how accurate they will be. You can make the circuitry show resolution of 1ppm, but thermal stability and hysteresis will mean you can't get useful accuracy at anywhere near that level.

I suggest you try to match the maximum full scale measurement to the load cell as the first step. If you only need to go to 1gram full scale then don't try to use a 500g load cell.