How did New York and New Jersey become English colonies?

The colony that would become New York was founded as New Netherland by Dutch settlers in the 1620s. They established New Amsterdam on Manhattan Island no long after. The colony thrived on the beaver trade with area Iroquois, but was in competition with the New England colonies just north of the region. In 1664, after the restoration of the British monarchy, English King Charles II, not recognizing the Dutch claim on the land (which was actually in a region long claimed by the English) granted it to the Duke of York, his brother and the future king James II. The Duke sent an expedition to seize the land from its Dutch governor Peter Stuyvesant, and renamed it New York after himself. He then granted the lands that are now New Jersey to two proprietors, Lords Carteret and Berkeley. Berkeley sold his lands to investors in England. This area, known as West Jersey, was heavily settled by Quakers. East Jersey, owned by Carteret, changed hands several times before uniting with the West (under the control of New York) in 1702. The combined colony gained separate status as New Jersey in 1728. However, the capitals of West and East Jersey, Burlington and Perth Amboy, respectively, remained dual seats of government until the Revolutionary era.