I don't think use of consistent weights and measures implies someone being in charge of those weights and measures.

I also don't think someone being in charge of weights and measures implies that same person/group being in charge of anything else.

The latter feels fairly obvious, for the former I imagine some generally agreed upon method for creating new weights and measures given some existing ones for calibration plus some base level of suspicion of new craftsmen/merchants until they are proven trustworthy by a subset of the existing trustworthy people who have their own weights/measures would do.

Also, as pointed out elsewhere in this thread anyone buying large amounts of whatever you're selling is going to have their own set of weights and measures, so your avenues for stiffing people without getting caught are pretty narrow.