The sensory traffic in Machine-to-Machine (M2M) communications has fairly heterogeneous service delay requirements. Therefore, we study the delay-performance of a heterogeneous M2M uplink from the sensors to a M2M application server (AS) via M2M aggregators (MA). We classify the heterogeneous M2M traffic aggregated at AS into multiple Periodic Update (PU) and Event Driven (ED) classes. The PU arrivals are periodic and need to be processed by a prespecified firm service deadline whereas the ED arrivals are random with firm or soft real-time or non real-time service requirements. We use step and sigmoidal functions to represent the service utility for PU and ED packets respectively. We propose a delay efficient multiclass packet scheduling heuristic that aims to maximize a proportionally fair system utility metric. Specifically, the proposed scheduler prioritizes service to ED data while ensuring that the PU packets meet their service deadline. It also minimizes successive PU failures for critical applications by penalizing their occurrences. Furthermore, the failed PU packets are immediately cleared from the system so as to reduce network congestion. Using extensive simulations, we show that the proposed scheduler outperforms popular packet schedulers and the performance gap increases with heterogeneity in latency requirements and with greater penalty for PU failures in critical applications.