[DW SD]

I would be concerned about friction within the scisscors throwing off of the measured numbers. I know my old scissor lift had plenty of friction in the mechanism. In fact, it wouldn't drop, if it had no weight on it (though the setup itself weighed hundreds of pounds. I think your 5% measurement error assumes no friction or equivalent amongst all four. I don't think that is a safe assumption.

Can't you do something simpler and more accurate with a balance beam and maybe a spring with known force constant? Or maybe something with a known counterweight? How about something like the scales at the doctor's office?