Experiment: We have a cylinder with a piston that is essentially weightless, frictionless, and exposed to atmospheric pressure. The cylinder has a volume of 2V, but half of it is filled with water and the other half is just filled with air that has the same density as the atmosphere. The water starts at barely above its freezing point (so its vapor pressure is 0). At this point, the piston is just floating above the water because the air pressure on the inside of the cylinder equals the air pressure on the outside.
Now, let's say we heated the water to 70 Celsius**. The piston would begin to expand because the water vapor pressure will go up. Eventually the rate of water vapor evaporating and water vapor condensing will reach an equilibrium and the piston would stop expanding. How do we know what the vapor pressure of the water is? The volume is now larger so the air is now less dense (so its partial pressure is less than 1 atm) which means the rest of the pressure is accounted for by the water vapor.
This is my guess for how scientists would calculate vapor pressure. But it honestly just seems a lot easier if we created a new term called "vapor height." Vapor height would be defined as the $V/A$ generated by a solution at a certain temperature.
**We are assuming the air molecules don't increase in temperature.