We present CoBLOC, the first interactive system for enforcing continuous group fairness over sliding windows in data streams. CoBLOC introduces block-level fairness, a fine-grained fairness model that exposes short-term disparities missed by window-level guarantees, and supports efficient real-time monitoring using compact sketch-based summaries. When violations occur, CoBLOC applies theoretically grounded stream reordering algorithms to restore fairness within the current window, while maintaining low-latency, high-throughput performance suitable for real-world streaming analytics. Through interactive demonstrations, CoBLOC also surfaces serendipitous moments where fairness adjustments become critical, provides intuitive explanations of its decisions, and recommends landmark sizes that best balance reordering cost and fairness in dynamic streaming settings.