Backscatter communication (BC) enables ultra-lowpower communications and allows devices to harvest energy simultaneously. But its practical deployment faces severe security threats caused by its nature of openness and broadcast. Authenticating backscatter devices (BDs) is treated as the first line of defense. However, complex cryptographic approaches are not desirable due to the limited computation capability of BDs. Existing physical layer authentication schemes cannot effectively support BD mobility, multiple attacker identification and attacker location tracing in an integrated way. To tackle these problems, this paper proposes BCAuth, a multi-stage authentication and attack tracing scheme based on the physical spatial information of BDs to realize enhanced BD authentication security for both static and mobile BDs. After initial authentication based on BD identity with its position information registration, preemptive authentication and re-authentication are performed according to spatial correlation of backscattered signal source locations associated with the BD. By exploiting clustering-based analysis on spacial information, BCAuth is capable of determining the number of attackers and localizing their positions. In addition, we propose a reciprocal channel-based method for BD reauthentication with better authentication performance than the clustering-based method for mobile BDs when the BDs is able to measure received signal strength (RSS), which also enables mutual authentication. We theoretically analyze BCAuth security and conduct extensive numerical simulations with various settings to show its desirable performance.