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Not a steam engine expert, but just thinking from a physics approach...You're looking for balance, or, rather, CG (center of gravity). The scale approach is going to be dicey at best. I would take a bit of track that covers the drivers and improvise a see-saw with the pivot under the center driver. CG is centered over the drivers when it balances on the pivot. If you're interested in total weight on the drivers, put the see-saw on the scale.
I've always though weight balancing was done to locomotives with sprung drivers.
And just to make everybody launch their lunch . As a trains drag pulls on the drawbar , and where the drawbar is attached vertically and what vertical slop it has , the static weight on drivers may differ when under load .
I think this is the perfect controlled opportunity to test out which thinking is correct.