Weather forecasting in Africa is hampered by sparse meteorological data and limited computational resources. This paper addresses these challenges by proposing lightweight deep learning (DL) for weather prediction and forecasting. We integrate active learning and transfer learning methods to enhance model training efficiency and accuracy. By focusing on the informativeness and representativeness of training samples, our approach significantly reduces the need for extensive and costly labeling. After training on a source dataset, model skills are transferred to target datasets, allowing for effective weather variable predictions with minimal data. Extensive experiments on three weather datasets demonstrate that our hybrid Transfer Active Learning method achieves similar classification accuracy compared to existing methods, using only 20% of the training samples. This study highlights the potential of advanced DL techniques to improve weather forecasting in Africa, despite the constraints of data scarcity and limited computational infrastructure.