A wireless sensor network (WSN) commonly requires lower level security for public information gathering, whilst a body sensor network (BSN) must be secured with strong authenticity to protect personal health information. In this paper, some practical problems with the message authentication codes (MACs), which were proposed in the popular security architectures for WSNs, are reconsidered. The analysis shows that the recommended MACs for WSNs, e.g., CBC-MAC (TinySec), OCB-MAC (MiniSec), and XCBC-MAC (SenSec), might not be exactly suitable for BSNs. Particularly an existential forgery attack is elaborated on XCBC-MAC. Considering the hardware limitations of BSNs, we propose a new family of tunable lightweight MAC based on the PRESENT block cipher. The first scheme, which is named TuLP, is a new lightweight MAC with 64-bit output range. The second scheme, which is named TuLP-128, is a 128-bit variant which provides a higher resistance against internal collisions. Compared with the existing schemes, our lightweight MACs are both time and resource efficient on hardware-constrained devices.