Existing self-supervised point cloud upsampling methods often depend on computationally intensive deep learning architectures, which demand extensive training time and resource consumption. To overcome these limitations, we propose LA-PUNet, a Lightweight Adaptive Point cloud Upsampling Network that significantly reduces model complexity while maintaining competitive performance. Our approach integrates farthest point sampling (FPS) and k-nearest neighbor (KNN) search to partition input sparse point clouds into spatially coherent blocks. These blocks are dynamically organized into ordered sequences based on spatial proximity and fed into an MLP decoder, which progressively predicts subsequent point distributions for adaptive upsampling. Experimental results demonstrate that our method achieves point cloud upsampling accuracy comparable to state-of-the-art self-supervised approaches while surpassing most supervised methods, despite requiring only 3 KB of parameters and a compact 0.07 MB model size, making it particularly suitable for resource-constrained scenarios such as edge devices or real-time applications.