Data centers are rapidly scaling and becoming more complex, making it critical to pinpoint where latency arises across the network protocol stack. Existing tools primarily measure RTT or single-layer delays, while multi-layer approaches are often invasive or limited. We present LatScope, a practical multi-layer latency analyzer that (i) matches packets across layers to compute accurate inter-layer delays despite retransmissions and out-of-order delivery, (ii) synchronizes server clocks using XDP to enable precise inter-server delay breakdowns, and (iii) controls overhead through selective data extraction. We validate LatScope across diverse environments and show how its insights can be applied effectively in cloud deployments.