Marble dissolves in acid
This video shows how Carrara marble reacts to acid (at 1.0 N, which is ~10000 times more aggressive than the worst acid rain!). Both hydrochloric (HCl) and nitric (HNO3) acids react with marble (CaCO3) and release CO2. You can see it bubbling through the acid as it runs down the stone.
In contrast, sulfuric acid reacts with marble to form gypsum (CaSO4), which forms a protective barrier on the surface of the stone, so that no visible damage occurs. Unfortunately, gypsum is also slightly soluble, so it doesn’t really protect monuments in the long run. Nevertheless, marble is less rapidly attacked by acid rain containing SO2 than NOx.