In a Victorian society, an engineer has come up with a clever boat lift for his canal, using counterweights. In order to work correctly and most efficiently, the operators will need to know how much each boat or barge actually weighs.
How could he do this? Clearly the obvious answer is to put the boat into a tank and see how much the water level rises; but the point of this system is to weigh the vessel for lifting - so any solution that involves picking the ship up isn't practicable.
Plimsoll lines could work; but not all boats would have them (and you'd need to establish how much the boat actually weighs before you can accurately apply these anyway.
The best I've been able to come up with so far is a dry-dock - float the ship in, empty the water out completely and then fill it up again with a specific amount; then measuring how high the water is should give an answer. But it's not a very elegant (or fast) solution - can anyone do any better?
Edit to answer some of the comments: This is a 'dry' boat lift, it which the vessel sits on blocks (similar to those in a dry dock) and is lifted out of the water; hence the need to know the mass (rather than a 'wet' lift where the mass would always be the same).