One thing that Jersey City and Brooklyn have in common is that they are both nextdoor neighbors with Manhattan. However, unlike Brooklyn, Jersey City sits right on the Hudson River, which as I understand it, made it a more favorable trading location with merchants from the interior of the country. Meanwhile Brooklyn sits on the East River which hasn't really been as economically important.
But Jersey City also shares many important pieces of transportation infrastructure with Manhattan connected New York to the rest of the country. The PATH Tubes, and the Holland Tunnel directly connected Jersey City to the Financial District in Lower Manhattan and Midtown, and they also help to connect Manhattan with New Jersey, and there for the rest of the continent.
However despite these benefits, Jersey City has always had a smaller population and has never really been as influential as Brooklyn has. Even before Brooklyn unified with New York, it was the fourth largest city in the United States while Jersey City was around 16th or 17th place.
Why didn't Jersey City experience nearly as much growth and development as Brooklyn did prior to its consolidation into New York City?
You asnwered the question yourself. Brooklyn is one of the largest area in terms of population in the whole country. JC is only a fraction. If it were to annex the towns and cities around it would exert more influence.