The proliferation of the Internet of Things (IoT) has led to a significant surge in the quantity of multivariate time series (MTS) data. Effective detection of anomalies within MTS data is crucial for modern industrial applications. However, existing anomaly detection methods face challenges due to the lack of labeled data, imbalanced data distributions, and complex temporal and metric relationships inherent in MTS data. Moreover, in IoT network environments characterized by heterogeneous resource constraints, achieving high accuracy in anomaly detection while minimizing latency and energy consumption remains a daunting task. To address these challenges, in this paper, we propose a Collaborative Anomaly Detection (ColAD) approach to optimize the trade-off between latency, energy consumption, and accuracy. Specifically, we design a fusion of parallel graph attention networks with temporal convolutional attention networks to learn the correlations within MTS data across different metrics and temporal instances via attention mechanisms. Furthermore, a variational autoencoder model with dynamic depth-awareness mechanism is proposed to accommodate heterogeneous resources. Additionally, ColAD leverages a deep reinforcement learning based selection method to dynamically determine the optimal layer for processing MTS anomaly detection tasks. Experimental evaluations demonstrate the efficacy of ColAD in achieving superior performance in terms of anomaly detection accuracy, latency, and energy consumption.