NYC would have rapidly died out had it not been sucking in people from the outside constantly because the death rates were vastly higher than the birth rates. One of the big infrastructure projects paid for by federal money raised by tariffs overwhelmingly on Southern goods was the NYC Sewer system. It took quite a while to construct it and get all the sewage out of town so there wouldn't be quite as much disease. For example, NYC had big cholera outbreaks in 1832, 1849 and 1866. The story in other big cities in the North wasn't that different at the time.
But you still didn’t tell us what the death rate was.
Looks like the big growth came between 1890 and 1930. That would pretty much coincide with the immigrant growth in the rest of the nation.
One of the big infrastructure projects paid for by federal money raised by tariffs overwhelmingly on Southern goods was the NYC Sewer system.
So you are saying that the Feds charged tariffs on Southern exports not on imports like the rest of the known world does. And then they gave the money to New York City to build the sewers. Is that it?