Does a skyscraper cause the whole island of Manhattan to sink, or just the land directly underneath it? If the latter, would we expect the result to be a bowl-l

Does a skyscraper cause the whole island of Manhattan to sink, or just the land directly underneath it? If the latter, would we expect the result to be a bowl-like structure where skyscrapers have pushed the middle down but the edges remain as they were? (Unless the edges also have skyscrapers on them I guess).