I think the weight mass method you are proposing is good; but you will need to set a spring or something to make the thing retract when the weight goes up and calibrating that spring will be a difficult task. The floaters move freely. Floaters have been used forever to meassure liquids specific gravities and that maybe the reason why.
Anyway if the weight (which is acctually a floater too) can be attached to the weighting system without affecting the meassurement then maybe it is another solution to the same problem.
A basic rule in measurements is that the meassuring system used should not affect the system being measured.