Safety, low-cost, small size, and Artificial Intelligence (AI) capabilities of drones have led to the proliferation of autonomous tiny Unmanned Aerial Vehicles (UAVs) in many applications which are dangerous, unknown, or time-consuming for humans. Deep Neural Networks (DNNs) have enabled autonomous navigation while using captured data by drone sensors as input to the model. Due to the extreme complexity of DNNs, cloud-based approaches have been highly addressed in which a drone is connected to the cloud and sends the data to the cloud, and takes the result. On the other hand, emerging tiny machine learning models and edge computing brings significant improvement in energy efficiency and latency with respect to cloud-based approaches. However, there is a trade-off in these two implementations for model accuracy, latency, and energy efficiency. For instance, applying tiny machine learning models leads to lower latency but it sacrifices model accuracy in comparison to cloud-based computing. To address these challenges, we consider multiple models and introduce a new approach named MLAE2 which applies Metareasoning approach for Latency-Aware Energy-Efficient autonomous drones. Metareasoning monitors parameters such as latency and energy consumption for different algorithms and chooses the appropriate algorithm due to the environmental situation changes. To Evaluate our approach we extract the power consumption and latency for both cloudbased computing and edge computing while deploying multiple models on a tiny drone named Crazyflie. The experimental results show that MLAE2 successfully meets the latency constraint while maximizing model accuracy and improving energy efficiency.