It is hard to measure weight in comparison to just measuring DC voltages.

So why are even quite expensive multimeters unable to measure voltages with really high precision (note precision - not resolution)? The multimeter can basically feed the voltage directly to the ADC, without any temperature-drifting sensor involved. It "only" need to care about the noise picked up in wires, and the quality of the voltage reference. And there are lots of reasonably priced ADC with very, good linearity.

When comparing with a multimeter - notice what happens when switching from DC mode to measuring AC, resistance, capacitance, temperature, ... The precision tends to drop because more electronics and sensors gets involved.