Note the +/-5% variation spans 2,000 years of Bronze Age history, so explanation doesn't need an explicit mechanism for "let's change the weights". (Although debasement was also a thing -- at least it was in the Roman Empire, and presumably people thought of it long before that).
I'd speculate there was no tendency for foreign trading partners to reconcile unequal measure systems, since neither party had the flexibility to change the weights used in their local markets. Or the markets of different foreign counterparties they also trade with. So regional differences could persist permanently, and would be recognized as such.
On the other hand, if merchants went out of their way to harmonize their standards (i.e. "let's take the arithmetic mean of our two weights and use that"), something like a network consensus could emerge. Non-systemic drift would scale down as 1/sqrt{ size of trade network }. (I wonder if Bronze Age traders ever tried analysis of algorithms? They probably lots of time of to think about things, on their endless trade roads).
I'd speculate there was no tendency for foreign trading partners to reconcile unequal measure systems, since neither party had the flexibility to change the weights used in their local markets. Or the markets of different foreign counterparties they also trade with. So regional differences could persist permanently, and would be recognized as such.
On the other hand, if merchants went out of their way to harmonize their standards (i.e. "let's take the arithmetic mean of our two weights and use that"), something like a network consensus could emerge. Non-systemic drift would scale down as 1/sqrt{ size of trade network }. (I wonder if Bronze Age traders ever tried analysis of algorithms? They probably lots of time of to think about things, on their endless trade roads).