I don't know about the rules in other states, but here in Montana propane meters are required to be certified for accuracy by the State Weights and Measures division, just like gas and diesel pumps are. They are also required to be temperature compensated, so the ambient temperature does not effect the amount dispensed.
I haven't had a cylinder filled by weight in years. Every place I have had them filled has had a meter, and it is dispensed and billed by the gallon.
Most dispenser locations open the spitter valve (or 80% valve, or whatever you want to call it), and fill until liquid appears or the OPD shuts off, whichever occurs first. Ideally, that should happen simultaneously, but few cylinders are "ideal".
I usually have mine filled at V-1 Propane/Amerigas, and that is the way they do it.