Load shedding is a technique employed by stream processing systems to handle unpredictable spikes in the input load whenever available computing resources are not adequately provisioned. A load shedder drops tuples to keep the input load below a critical threshold and thus avoid unbounded queuing and system trashing. In this paper we propose Load-Aware Shedding (LAS), a novel load shedding solution that, unlike previous works, does not rely neither on a pre-defined cost model nor on any assumption on the tuple execution duration. Leveraging sketches, LAS efficiently builds and maintains at runtime a cost model to estimate the execution duration of each tuple with small error bounds. This estimation enables a proactive load shedding of the input stream at any operator that aims at limiting queuing latencies while dropping as few tuples as possible. We provide a theoretical analysis proving that LAS is an (ε, δ)-approximation of the optimal online load shedder. Furthermore, through an extensive practical evaluation based on simulations and a prototype, we evaluate its impact on stream processing applications, which validate the robustness and accuracy of LAS.