Answer:
The reason support for ratification won out in New York despite the fact that Antifederalists controlled most of the state's territory is likely due to a number of factors, including the persuasive arguments of Federalists, changes in public opinion, and the influence of political and economic leaders.
The Federalists made a strong case for ratification, highlighting the benefits of a strong central government and the dangers of the existing Articles of Confederation. They may have also won over some Antifederalists with compromises, such as the addition of the Bill of Rights.
Additionally, the changing economic and political landscape may have played a role in shifting public opinion. For example, the threat of rebellion by farmers in western Massachusetts (Shays' Rebellion) highlighted the weaknesses of the existing government and may have convinced some Antifederalists of the need for a stronger central government.
Finally, the influence of political and economic leaders, such as Alexander Hamilton, may have also played a role in securing ratification. Hamilton was a strong advocate for ratification and worked to convince New York's political and economic elite of the benefits of the new constitution.
In the end, it's likely that a combination of these factors led to the ratification of the Constitution in New York, despite the fact that Antifederalists controlled much of the state's territory.