Measuring weight is not a single procedure, it's many procedures that agree, because they're measuring something that "exists" in some sense.

I suspect that your definition of "exists" is circular. How can we tell if something exists other than by having "procedures that agree"?

That's how electricity was discovered

What was discovered is "many procedures that agree", like rubbing some materials resulting in sparks, similar sparks between objects during a thunderstorm, etc. These were eventually abstracted into the concept of electricity, which ended up being very useful in its predictive power and practical applications.

So I'd go the other way round, and first try to figure out which quantities "exist", regardless of usefulness.

...And you do that by finding the "procedures that agree".

Oh, and I find the content of your link rather presumptuous due to its failure of imagination. I can easily imagine that "their" equivalent of math, physics or comp sci has nothing in common with ours.