Recently, learning signed distance functions (SDFs) from point clouds has become popular for reconstruction. To ensure accuracy, most methods require using high-resolution Marching Cubes for surface extraction. However, this results in redundant mesh elements, making the mesh inconvenient to use. To solve the problem, we propose an adaptive meshing method to extract resolution-adaptive meshes based on surface curvature, enabling the recovery of high-fidelity lightweight meshes. Specifically, we first use point-based representation to perceive implicit surfaces and calculate surface curvature. A vertex generator is designed to produce curvature-adaptive vertices with any specified number on the implicit surface, preserving the overall structure and high-curvature features. Then we develop a Delaunay meshing algorithm to generate meshes from vertices, ensuring geometric fidelity and correct topology. In addition, to obtain accurate SDFs for adaptive meshing and achieve better lightweight reconstruction, we design a hybrid representation combining feature grid and feature tri-plane for better detail capture. Experiments demonstrate that our method can generate high-quality lightweight meshes from point clouds. Compared with methods from various categories, our approach achieves superior results, especially in capturing more details with fewer elements.