Europeans had various ways of overpowering colonial natives; their arsenal was not limited to physical weapons. How else did they overpower Native peoples?
First, we should remember that Europeans "overpowered" Natives in the long term. In the short term, for many colonists, it was Indian peoples who held most of the power and dictated the terms of colonial-Native interaction. Some other strategies that Europeans used to gain more power in their dealings with Indians were as follows.
First, Europeans sought to exploit pre-existing rivalries and hostilities between Indian peoples, in what was conceived as an effort to "divide and conquer." For example, Cortes's famous conquest of the Aztecs would not have been possible without the assistance of the many Indian peoples who lived around the mighty Aztec Empire and resented its control.
Second, Europeans tried to gain entry into Indian society by marriage and other means. English colonists in the Southern colonies were particularly adept at this, especially merchants. In so doing, they formed the kinship relationships that were essential to Native diplomacy.
Third, Europeans tried to make treaties signed by one Indian group binding on others. That is, they allowed some Indians to speak for others who had not in fact vested them with that authority. This policy persisted into the late nineteenth century, when it was pursued with the Sioux and other Plains Indians.
Again, we should not imagine that Indians were passive or helpless in this process. They sought Europeans as allies and trading partners, and they could cleverly "play off" one European nation against another by making what seemed to Europeans to be conflicting treaty agreements. They acted within their cultural frameworks to make decisions that seemed the right ones at the time.