Okay, this was the really tough one. I looked at the Empire State Building, which weighs 350,000 tons. I looked at the average house, which weighs 70 tons. But most of the 47,000 buildings in Manhattan are neither the Empire State Building or a family home. So I reached out to an engineer friend of mine, and she told me that the best way to make a reasonable guess is to go by floor. Here’s what she said:
"For buildings over 30 stories, use 3,000 tons per floor. Buildings under 30, use 200. That's an arbitrary choice of using 30 floors as the breaking point. but based on the spreadsheet [available here], there are 24,373 total floors in buildings over 30 floors (604 buildings), and 225,203 floors in buildings under 30 floors (39,954 buildings)."
That gets us a ridiculous total of 118,159,600 tons of buildings.