The sulfur is on the plates. The different materials of the plates, the sulfur deposition on the plates, and the water, when fed a small electrical current, form an exothermic chemical reaction, adding sulfur to H2O resulting in H2SO4 (sulfuric acid) and PbO2.
I think you are having a problem with the quantity of the acid being different with the quantity of non-acidic water added back into the battery case, not the basic chemistry. As you can see in the prior link I posted, the electrolyte is not 100% sulfuric acid. It is actually dilute acid.
Further reading at
Battery U