In the midst of reading the history of the Soderberg number, I was amused to read upthread:
P.S. I want to know how @Arellcat would do it.
Having given it some consideration this evening I would take one good quality spoke from an Ordinary, nominally 12g and 0.7m long, and construct a single 0.5m long wire with a hook at each end. One hook is attached to the ceiling. The other hook is formed firstly to suspend the bicycle by either the saddle or top tube and the free end of the hook formed to provide a horizontal marker point that engages with the micrometer. Set the micrometer to a mid-scale value, say 10.000mm and ensure that the travelling end rests against the upper surface of the marker point. Then hang the bicycle (gently), adjust the micrometer until the marker point is reached, and take the difference in readings.
Given typical values for Young's Modulus of 210 GPa and a bicycle weight of 15kg, the resulting elongation would be approximately 0.06mm, which is well within the discrimination of the micrometer. The pedant might advise to calibrate the spoke first, in order to determine Young's Modulus exactly.
Then, for a bike of unknown weight, the tensile force applied to the spoke may thus be determined as the measured elongation multiplied by Young's Modulus multiplied by the cross-sectional area of the spoke, divided by the original length; and the weight of the bike is simply the force divided by g (9.81m/sec squared; or about 10).