For the OP original concern, if he paid by gallons and got the gallons charged all is ok. if he paid by weight (never seen that but possible) and got the weight he paid for all is ok.
If he paid by gallons and then weighs the cylinder, depending on the mix of propane and butane, trying to figure out if it was correct is not real possible unless he knows the exact propane/butane mix, cylinder weight beforefill etc.
In virtually all places I've filled tanks, your buying LPG, if you read the fine print. That covers a variety of liquid petroleum gas mixes, usually mostly propane, but can also contain some % butane and other gases. The weight will vary depending on the mix. (as well as energy content, and suitability for low temp use)
"Liquefied petroleum gas (LPG or LP gas) is a fuel gas which contains a flammable mixture of hydrocarbon gases, specifically propane, propylene, butylene, isobutane, and n-butane.
In the northern hemisphere winter, the mixes contain more propane, while in summer, they contain more butane"
Most, if not all states have very tight regulations and annual or more often checks on gas/diesel/propane pumps. If they are off, store is in BIG trouble.
Personally, while on a very few occasions they did the fill stopping at a certain weight, I was still charged by gallons on the pump.