In high-speed networks, real-time monitoring of heavy flows is vital for reliable communication and rapid anomaly detection (e.g., DDoS). This task is challenging due to limited fast memory and the inefficiency of existing sketches, which struggle with skewed traffic and hardware constraints. We present Harmonia, a sketch for efficient and accurate heavy flow detection. Unlike prior methods that use multi-dimensional features at high memory cost, Harmonia leverages traffic skewness: once a flow’s frequency exceeds a threshold, it is deemed heavy and protected from eviction during hash collisions. Implemented on CPU, programmable switches, and FPGA, and evaluated on real-world traces, Harmonia improves detection accuracy by up to 27.83% while requiring at most 18% and 10% of available resources on switches and FPGAs.