Complex Event Recognition (CER) systems detect event oc- currences in streaming time-stamped input using predefined event patterns. Logic-based approaches are of special interest in CER, since, via Statistical Relational AI, they combine uncertainty-resilient reasoning with time and change, with machine learning, thus alleviating the cost of manual event pattern authoring. We present WOLED, a system based on Answer Set Programming (ASP), capable of probabilistic reasoning with complex event patterns in the form of weighted rules in the Event Calculus, whose structure and weights are learnt online. We compare our ASP-based implementation with a Markov Logic-based one and with a crisp version of the algorithm that learns unweighted rules, on CER datasets for activity recognition, maritime surveillance and fleet management. Our results demonstrate the superiority of our novel implementation, both in terms of efficiency and predictive performance.