Self-contact variable stiffness (SVS) metamaterial offers specific patterns of elastic strain energy storage by changing its force-transferring path. The change of the elastic strain energy storage patterns further influences the stiffness variation of the SVS metamaterials. However, challenges still arise because typically fabricated SVS metamaterials inevitably contain structural irregularities, eccentricities, and defects. These microstructural imperfections impede the stable generation of designed strain energy storage patterns in the metamaterial, implying that the SVS metamaterials cannot achieve expected stiffness variations. To address this burning question, an SVS metamaterial/meta-structure design paradigm with eccentric unit designs is proposed, which can realize both stable stiffness variations and high load-bearing. The theoretical, simulation, and experimental results demonstrate that the SVS chain meta-structure achieves ≈110 times stiffness variation between the low and high loading conditions. Its load-bearing can reach more than 1500 N when the meta-structure falls into the high stiffness stage. Furthermore, some typical functions are demonstrated using the stability-enhanced SVS metamaterial, including customized mechanical protections for human joints and information transformation regulated by remote mechanical input signals. The results can provide a useful solution for generating a more feasible stability-enhanced SVS metamaterial/meta-structure and promote their potential applications in aerospace, medical devices, and robotics.