Addressing the inherent low acquisition frequency limitation of 3D LiDAR to achieve high-frequency output has become a critical research focus in the LiDAR-Inertial Odometry (LIO) domain. To ensure real-time performance, frequency-enhanced LIO systems must process each sweep within significantly reduced timeframe, which presents substantial challenges for deployment on resource-constrained platforms. To address these limitations, we introduce SR-LIO++, an innovative LIO system capable of achieving doubled output frequency relative to input frequency on resource-constrained hardware platforms, including the Raspberry Pi 4B. Our system employs the previously proposed sweep reconstruction methodology to enhance LiDAR sweep frequency, generating high-frequency reconstructed sweeps. Building upon this foundation, we propose a caching mechanism for intermediate results (i.e., surface parameters) of the most recent segments, effectively minimizing redundant processing of common segments in adjacent reconstructed sweeps. This method decouples processing time from the traditionally linear dependence on reconstructed sweep frequency. Furthermore, we present a quantized map point management based on index table mapping, significantly reducing memory usage by converting global 3D point storage from 64-bit double precision to 8-bit char representation. This method also converts the computationally intensive Euclidean distance calculations in nearest neighbor searches from 64-bit double precision to 16-bit short and 32-bit integer formats, reducing computational cost. Extensive experimental evaluations across three distinct computing platforms and four public datasets demonstrate that SR-LIO++ maintains state-of-the-art accuracy while substantially enhancing efficiency. Notably, our system successfully achieves 20 Hz state output on Raspberry Pi 4B hardware.