To measure resistance as low as 1 mR with precision, I would use a 10A current source for the lowest range.
(four wires measurement of course !)
Few milliamperes is sufficient: https://www.eevblog.com/forum/projects/hx711-based-milliohm-meter/msg782192/#msg782192
How could you measure 1mR with 1% precision if your project has:
- Initial drift was 3 milliohms
- After initial drift, the variance was +/- 0.5 milliohms
- Measurement current is in range 5mA - 10mA.
The idea of my posting was that 10A is not needed in order to be able to measure milliohm resolution, only few milliamperes is sufficient. Dannyf did some further development in the discussion thread and he was able to get the accuracy good enough for milliampere accuracy. The HX711 has some temperature drift issues what was found out, but the temperature effect was few milliohms at worst, and the error due to the temperature drift got less after the HX711 was kept in constant temperature.
The OP wanted to have a milliohm resistor measurement device with a range 1 milliohm ... 1 ohm with 1% accuracy. If the accuracy of 1% means the accuracy over full measurement range of 1 ohm, then the required accuracy should be better than +/- 5 milliohms which can be achieved even with the cheap, non-compensated HX711. If one replaces the HX711 with a better ADC or builds a simple temperature control for the HX711, the measurement accuracy can be easily in range of +/- 0.1 milliohms, which is pretty good. However, the dannyf's idea to use a cheap HX711 ADC with ratiometric measurement and small measurement current with a high resolution A/D-converter was a clever solution.
Edit: Some microcontrollers have pretty high resolution on-chip A/D-converters. For example, the Psoc5 LP devices have a 20-bit differential input delta-sigma ADC. Unfortunately I do not have time atm to give it a try how good milliohm meter could be built using the the Psoc5 LP device, using ratiometric measurement, chopped stimulus current and synchronous detection. If the accuracy of the on-chip reference voltage is not good enough, one can use an external reference voltage for improved performance.