I think it's much easier to visualize the way buoyancy, gravity and displacement works if you think in reverse.
Lets take our imaginary model submarine. For arguments sake we will say it is made from brass (a material about eight times the density of water) and let us take for granted that we have calculated the displacement of the structure above the intended surfaced waterline is 100ml, which equates to a 100 grams of (fresh) water or approximately 800 grams of brass.
In order for our submarine to float at the right waterline, we would need to provide buoyancy to support 800 grams, including the ballast tank, and this would all be placed below the waterline. The ballast tank would equal the displacement of 100ml.
If you used weight, then you would have built an 800ml ballast tank, and most certainly your boat would submerge, albeit with just a tiny amount of water in the tank.
In practice trying to calculate the right amount of volume for your tank using mathematics and a pocket calculator is very difficult unless the boat you are modeling is of extremely simple shape. The best way to find the volume is to calculate a rough estimate, then use empirical methods and even then you should allow yourself 10-20% over to account for different water density and mineral content.