How did the iroquois eventually upset the balance of power between the french and the british?

In their relations with white settlers, the Iroquois from the start played the role of an independent power. During the colonial period they held the balance of power between the French and English, particularly in the area around the Canadian border.

With few exceptions, chiefly factions of the Mohawk and Cayuga, who came under the influence of French Jesuit missionaries, the Iroquois allied themselves with English interests. They bitterly opposed the extension of French settlement southward from Canada, and they were responsible for preventing the English colonies from being flanked on the west by the French. 

Ithink the answer is baby boomers ?

Ithink the answer you are looking for is (b).