Constant input to A0 pin from HX711 amplifier and load cell

And I tenuously understand how using PID code for analog input with a digital device would not work.

In your posted code, the PID algorithm is taking its input via the following line:

  Input = analogRead(inputPin);

Change that to something like (substitute the appropriate variable name):

  Input = value_obtained_from_HX711;

Be sure to carefully study the PID documentation for the allowable range of PID input values, PID output values, and how to set the Kp, Ki and Kd constants.