Yes, it will work, you have the basic idea figured out. The other posters mentioned the details that will cause inaccuracy (although nobody mentioned friction). Maybe for your use it wont matter, maybe it will but now that you know the problems, you can get around them with the understanding of the issues. Maybe its as simple as attaching a chain to a single spot and lifting to a certain lift height. That would eliminate most of the problems but would be inconvenient. But it would work.
As for the math, look at the test machine I posted the link to. Thats simple math where the area of the cylinder will be the same pressure applied to the gauge. When the weights lift, you know you are applying the proper known pressure on the gauge. Example: if the area of the cylinder is 1 square inch, putting 10 pounds of weight on the test machine will show 10 PSI on the gauge... or it SHOULD show 10PSI if its a good gauge. Thats the math, simple. For your loader you have geometry that comes into play, it would be easier to just do known test weights and record your readings and make a chart of that info. What you would have then is a custom load chart like they put in forklifts and old cranes but your chart would be actual weight, not safe lifting loads at certain extensions. But it WILL work, the math works and people have made machines as proof that it works.
The math also works in reverse too. If you know how many PSI your hydraulic pump puts out, you know the size of your cylinders and can figure out the leverage of your loader, you can calculate what the tractor will lift. Sorry for the long answer but yes, it will work.
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Today's Featured Article - Hydraulics - Cylinder Anatomy - by Curtis von Fange. Let’s make one more addition to our series on hydraulics. I’ve noticed a few questions in the comment section that could pertain to hydraulic cylinders so I thought we could take a short look at this real workhorse of the circuit. Cylinders are the reason for the hydraulic circuit. They take the fluid power delivered from the pump and magically change it into mechanical power. There are many types of cylinders that one might run across on a farm scenario. Each one could take a chapter in
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