Complex sentence: New York, as America's largest city exponential growing during the 19th century (doubling from 1800--20 and again by 1840 to 300 000), saw the beginnings of a homosexual subculture concomitantly growing with the population.
Split into simpler sentences: New York, as America's largest city, almost doubled population during the first half of the 19th century (from 1800--20 and again by 1840 to 300 000). The city saw the beginnings of a homosexual subculture concomitantly growing with the population.