maybe something like this: https://www.erowid.org/archive/rhodium/chemistry/equipment/s... https://www.erowid.org/archive/rhodium/chemistry/equipment/s...
I found some old emails about the scale from 2005/6 but can't find the link and it would probably be gone anyways.
You measure the change in resistance with a wheatstone bridge tuned correctly.
You basically just need a strain gague (a few dollars), 4 resistors, an op-amp, and a microcontroller with an ADC.
Calibration is important and you'll run into things like the metal bar creeping, permanently bending as a result of weight being put on and off.
But also, milligram accurate scales are $20 on Amazon https://www.amazon.com/GRAM-PRES-Precision-Milligram-Reloadi...
(This one might be fine? It does claim to have a 50.000g calibration weight, which is a good sign, but it doesn't say anything about metrological traceability, which is a bad sign.)
A US$2 quartz watch measures time to 5½ significant figures, US$10 multimeters routinely measure voltage to 4½, and US$5 GPS receivers can provide you with time measurements accurate to 40ns that inherit the drift of world metrology standards, a precision of 16 significant figures if you are measuring a long enough time interval (over 10 years).
It's a $20 scale, if you had need of metrology you wouldn't be buying a $20 scale. Most of us do not need metrology. I want to make small amounts of pickles with perhaps unreasonably precise measurements of salt at scales where half a gram or maybe a tenth of a gram is significant.
If you have some way to cut a precise shape out of some kind of metal sheet of well-controlled thickness, could you cut out a milligram precision bismar balance or steelyard?
In general if you want a precise and accurate strain gauge you’ll be paying a lot for it, especially for one that doesn’t need to be recalibrated before every use and after nearly every measurement.
[1] https://www.mccsemi.com/pdf/ComponentWeightInformation.pdf
They don't tend to use strain gauges I think.