In this paper, we present an adaptive reweighted sparse belief propagation (AR-SBP) decoder for polar codes. The AR-SBP technique is inspired by decoders that employ the sum-product algorithm for low-density parity-check codes. In particular, the AR-SBP decoding strategy introduces reweighting of the exchanged log-likelihood-ratio in order to refine the message passing, improving the performance of the decoder and reducing the number of required iterations. An analysis of the convergence of AR-SBP is carried out along with a study of the complexity of the analyzed decoders. Numerical examples show that the AR-SBP decoder outperforms existing decoding algorithms for a reduced number of iterations, enabling low-latency applications.