Although foundation models have demonstrated remarkable success in general domains, the application of these models to electroencephalography (EEG) analysis is constrained by substantial data requirements and high parameterization. These factors incur prohibitive computational costs, thereby impeding deployment in resource-constrained clinical environments. Conversely, general-purpose automated machine learning frameworks are often ill-suited for this domain, as exploration within an unbounded programmatic space fails to incorporate essential neurophysiological priors and frequently yields solutions that lack scientific plausibility. To address these limitations, we propose NeuroWeaver, a unified autonomous evolutionary agent designed to generalize across diverse EEG datasets and tasks by reformulating pipeline engineering as a discrete constrained optimization problem. Specifically, we employ a Domain-Informed Subspace Initialization to confine the search to neuroscientifically plausible manifolds, coupled with a Multi-Objective Evolutionary Optimization that dynamically balances performance, novelty, and efficiency via self-reflective refinement. Empirical evaluations across five heterogeneous benchmarks demonstrate that NeuroWeaver synthesizes lightweight solutions that consistently outperform state-of-the-art task-specific methods and achieve performance comparable to large-scale foundation models, despite utilizing significantly fewer parameters.