The assumption that you are making is that the skimmer pulls the same amount of waste out per unit time, independent of the concentration of waste. That is wrong.
The amount of waste the skimmer pulls out is proportional to the concentration of waste.
Think of it this way. You put 1,000 gram of waste into a 1,000 litre tank, and 1,000 gram into a 2,000 litre tank.
So the first tank has a concentration of 1 gram per litre, the second 0.5 grams per litre.
Say the first tank has a skimmer which put through 1,000 litres an hour, and say it removes 100% of the waste going through it. It's going to remove 1,000 grams of waste in an hour of running.
Now the second tank has that same skimmer on it (pumping through 1,000 litres as before, removing 100% of the waste passing through it), then it is going to pull out only 500 grams of waste in an hour of running.
So extrapolating this through the dynamics of the system, it means that the concentration of waste in the water is independent of the total water volume of the system. It is a function of skimmer parameters.