Another way to guesstimate the operating weight of a steam locomotive is by the tractive effort. Typically, a steam locomotive's weight on drivers is about four times its tractive effort. Then you have to add the weight carried by any leading or trailing truck. Tank type engines add another consideration in that it must carry enough weight on drivers in proportion to maximum tractive effort even when the fuel tank/bunker and water space are nearly empty. Too much tractive effort versus weight on drivers and the engine will slip too much. Typical adhesion to the rail is about 25% (a factor of four) but can easily range from 20% to 30% for steam and early diesel. A tank engine with a full load of fuel and water will be less likely to slip under poor rail conditions because of the extra weight on drivers.
With a tractive effort of 3,540 then the minimum operating weight of an 0-4-0 should be around 14,160. If Betsy weighs 12,000 dry per the crane scale, then you only need about 270 gallons of fuel or water in the boiler and saddle tank to bring it up to the minimum theoretical weight of 14,160. Not to mention sand, tools and crew so likely closer to 15,000 pounds minimum operating weight. To get to a maximum operating weight of 20,000 would only need to carry another 625 gallons of fuel (oil in this case) or water in the tanks.
In the right perspective, the above numbers being discussed are plausible in long established theory.