Electrical – Is it possible to use the HX711 as an amplifier without using its ADC capabilities

My approach to this would be to get the ADC working by reading values in the Altera debugger first. It looks like the chip spontaneously takes samples and declares itself "ready" every 100ms. So you need to build a system which looks for that signal and starts shifting in the data at the appropriate speed (1MHz SPI). There's a slight wrinkle in that you have to send 25,26 or 27 clock pulses to configure its behaviour. Once you've got 24 bits in a shift register, you should be able to use the Altera toolchain (Chipscope?) to show you this without having to build some kind of user interface yet.

Then you have to calibrate it, and work out what logic to apply as a result.

As for physical connection, it ought to just connect directly to two GPIOs - check the voltages, and keep wires short.

According to my calculations, there is a gain in this amplifier of almost 3800. Your 4.7mV offset implies < 2uV of input offset voltage, which is really very good for any amplifier.

Instrumentation amplifiers can have offset voltages lower than this under ideal conditions but across temperature they will not be quite as good.

My question would be, why do you want to null this tiny offset when it refers to a tiny input offset?

See my comment that R11 and R13 should be the same; this is quite likely the cause of offset in the simulation (I may run it later when I have some time)

If you really need to offset this output, then I would use a precision reference and a follower into the final output amplifier.

Note that the tolerance build-up of your components in a real application will very probably dwarf this offset you have.

To overcome this, you may wish to use a precision instrumentation amplifier.

HTH