The term originated in Port Royal Jamaica in the 1600s when pirates were constantly looking for ships to loot and their guns were very primitive. As a result, pirates could shoot only once before a long reloading process. Consequently, they needed to carry a gun in each hand, and also perhaps in each pocket. For extra power, they would also hold a knife between their teeth. So to be 'armed to the teeth' means to carry the maximum number of weapons possible
Source: Times of India
Source: Times of India