A tenant hosted by a cloud platform typically runs a lot of applications, each of which not only has its own service capacity but also differs in revenue or business importance. Thus we argue that it is crucial for a cloud platform to provide fine-grained and application-aware performance monitoring for each tenant, rather than current monitors that can only handle overall metrics. In this paper, we propose CloudWatch+, a tool that focuses on detecting the latency of web-based applications. A cloud platform equipping with CloudWatch+ can automatically learn and distinguish web-based applications it is hosting, and detect latency anomalies for each application based on its own status. Our evaluation using the real data from a cloud platform with over 200 tenants demonstrates that the detection results of CloudWatch+ are more detailed than those of Amazon CloudWatch, which misses most alarms while some tenants' specific applications experience bad performance. Meanwhile, CloudWatch+ is also realtime and light-weight.