Resource management for cloud-native microservices has attracted a lot of recent attention. Previous work has shown that machine learning (ML)-driven approaches outperform traditional techniques, such as autoscaling, in terms of both SLA maintenance and resource efficiency. However, MLdriven approaches also face challenges including lengthy data collection processes and limited scalability. We present Ursa, a lightweight resource management system for cloud-native microservices that addresses these challenges. Ursa uses an analytical model that decomposes the end-to-end SLA into per-service SLA, and maps per-service SLA to individual resource allocations per microservice tier. To speed up the exploration process and avoid prolonged SLA violations, Ursa explores each microservice individually, and swiftly stops exploration if latency exceeds its SLA. We evaluate Ursa on a set of representative and end-to-end microservice topologies, including a social network, media service and video processing pipeline, each consisting of multiple classes and priorities of requests with different SLAs, and compare it against two representative ML-driven systems, Sinan and Firm. Compared to these ML-driven approaches, Ursa provides significant advantages: It shortens the data collection process by more than 128×, and its control plane is 43× faster than ML-driven approaches. At the same time, Ursa does not sacrifice resource efficiency or SLAs. During online deployment, Ursa reduces the SLA violation rate by 9.0% up to 49.9%, and reduces CPU allocation by up to 86.2% compared to ML-driven approaches.