The weights only have an error of 5%, which is a standard deviation of about a gram at any particular point in time. Manufacturing error is a far more parsimonious explanation.
The article's argument is that a state run distribution would have eliminated those manufacturing errors, but they could have just used them to their advantage.
The principle of parsimony applies here. Explanations that don't require centralized bronze age kingdoms everywhere, formal standardization of weights, and thousands of years of no one conducting long distance trade are more parsimonious than those that do.
One of the issues with archaeology is that it's easy to come up with thousands of plausible explanations for any particular set of data. Parsimony and other tools are essential to winnowing things down a bit.
>Explanations that don't require centralized bronze age kingdoms everywhere, formal standardization of weights, and thousands of years of no one conducting long distance trade are more parsimonious than those that do.
We have ample evidence of all three of those existed to some degree, and that's why the idea that the measurements were decreed has been the predominant explanation for a while now. I think this one piece of evidence could be explained within the current hypothesis.