Totally got this one. Native Staten Islander here, who has done research. I'm on my phone, so I cannot provide links at the moment though.

First, one has to realize that Staten Island is the least populous borough--I think the current population is only about 500-600k. Staten Island historically has also been sparsely populated in relationship to the rest of the city. This is very much a result of the geography of the island. While not a problem now, Staten Island had difficult terrain to live: rocky hills (made of Serpentine rock) and wetland/marshland further south. This made it very difficult for many people to have farms, and the surroubdi by waterways (Arthur Kill and Kill van Kull) would have been too narrow and shallow for large scale exporting.

Staten Island, therefore, remained as a sparsely populated farmland for a long time. Similarly, it's distance from Brooklyn and Manhattan made it difficult for regular travel and inter-county trade. There were ferries (such as Cornelius Vanderbilt's, which started him on to his fortune and later evolved into the Staten Island Ferry), but they were not as many as would have been needed for large scale trade.

That being said, Staten Island was always integrated with New York rather than New Jersey. Fort Wadsworth was paired with Fort Hamilton in Brooklyn to protect the harbor. Staten Island served as a quarantine for sick immigrants. It's proximity to the harbor allowed it to profit from New Yorks trade as well.

When New York became a city, Staten Island was the last to join in 1898. Many Staten Islanders were not happy (and many are still not to this day).

The first easy access to the borough came in 1963, when the Verrazano Narrows bridge was completed. That started Staten Islands population growth. New Yorkers saw the free land and the proximity to the city (now with bridge access) and began to move there for residential purposes, while working in the rest of the city.