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Classification tasks on ultra-lightweight devices demand devices that are resource-constrained and deliver swift responses. Binary Vector Symbolic Architecture (VSA) is a promising approach due to its minimal memory requirements and fast execution times compared to traditional machine learning (ML) methods. Nonetheless, binary VSA's practicality is limited by its inferior inference performance and a design that prioritizes algorithmic over hardware optimization. This paper introduces UniVSA, a co-optimized binary VSA framework for both algorithm and hardware. UniVSA not only significantly enhances inference accuracy beyond current state-of-the-art binary VSA models but also reduces memory footprints. It incorporates novel, lightweight modules and design flow tailored for optimal hardware performance. Experimental results show that UniVSA surpasses traditional ML methods in terms of performance on resource-limited devices, achieving smaller memory usage, lower latency, reduced resource demand, and decreased power consumption.