Both the aztec and the inca created formidable empires. what weakness if any did these empires have>

First of all, the Aztecs and Incas were isolated in the "new world" and didnt have contact with the other cultures around the world like Asians, Europeans and Africans. For example, the Chinese are the ones who invented gun powder and the idea spread throughout the rest of the world and was eventually used to propel ammunition (guns). 
The isolation also made Aztecs and Incas susceptible to European diseases which they had never been exposed to. A large percentage of those populations died and were weakened before the fighting even began. They also didnt have horses or most common beasts of burden because they simply didnt exist in South America. The Incas and Aztecs were two of the most powerful empires in their respective regions and like most empires, they had their share of enemies. Cortez formed allies with neighboring tribes which played a huge role in defeating the Aztecs, Pizzaro did the same in South America.