Effective system resource management is key to delivering high performance stream processing. Stream processing engines (SPEs) rely on their host operating system (OS) for managing compute and memory resources, but this is inefficient as the OS is not stream-aware, i.e., the OS does not understand the streaming dataflow or pipeline state in how they relate to the resource requirements of stream processing. Additionally, the lack of stream-awareness inhibits adaptive resource allocation in response to dynamic workload changes. We present Enjima, a modern SPE designed for scale-up on a single machine through adaptive stream-aware management of memory and compute resources. Enjima's eager, cache-aligned, block-based memory management avoids memory allocation on the critical path of system execution while providing efficient data transfer of events between streaming operators. Its variable batching forms event batches based on pending inputs and available output memory, reducing batching delays and memory accesses to enhance system performance. Enjima integrates a stream-aware, state-based operator scheduler that leverages fine-grained operator and pipeline metrics such as operator cost, selectivity, and latency gradient to optimize for both latency and throughput, enabling significant performance gains and rapid adaptation to dynamic workloads. Evaluation against state-of-the-art systems shows that Enjima achieves up to 6.3× higher throughput and up to three orders of magnitude lower latency through integrated stream-aware memory and CPU resource management.