Fun fact: the Empire State building weighs almost exactly the same as the rock excavated to make its basement. So that building, at least, is not contributing to the island sinking.<p>It also makes an interesting way point to solving the Fermi problem of estimating the building's weight: first estimate the footprint, then estimate the depth of the basement, then calculate the mass of that much rock at 3-4 metric tons per cubic meter.
Oh, that silly paper. Discussed previously, although I can't find the reference. This is a non-problem for Manhattan, where bedrock is close to the surface and it's hard New York Rock. It's a problem for some buildings built with on friction piles, like that tower in San Francisco. It's also a problem for low-lying areas where there's been too much oil extraction, such as parts of Louisiana.