Weighing is old; weighing at home is not. For most of the history of cookery, domestic quantities were handled by volume, by eye and by comparison, and the balance belonged to the shop, the pharmacy and the counting house.
The kitchen scale is what happened when spring mechanisms made accurate weighing cheap enough to sell to households, and it arrived carrying the habits of the trade it came from.
Balance, spring and strain gauge
Three mechanisms cover almost the whole story. The balance compares an unknown against known weights and is extremely accurate and slow. The spring scale reads deflection against a calibrated face and is fast, cheap and less precise. The strain gauge converts deflection into an electrical signal and made a digital readout possible.
Each mechanism produced a different object on the counter, and the shape of the scale in a period photograph dates the kitchen fairly reliably.
Volume against weight
The persistence of volume measurement in some cooking traditions and weight in others is not an accident of taste. It follows what equipment was cheap and available when each tradition's standard cookbooks were written, and those books then fixed the convention for generations.
This is why converting between two recipe traditions is genuinely awkward. The two systems are not describing the same property, and a cup of a compressible ingredient is a range rather than a figure.
What a scale actually settles
A scale answers one narrow question precisely: how much mass is on the pan. It says nothing about composition, preparation or anything downstream of the counter, and it was never built to.
That narrowness is the tool's virtue. A device that measures one property well is more useful than one that gestures at several, and the kitchen scale has survived a century of kitchen fashion largely on that basis.