Pick-and-place is essential in diverse robotic applications for industries including manufacturing, and assembly. Soft grippers offer a cost-effective, and low-maintenance alternative for secure object grasping without complex sensing and control systems. However, their inherent softness normally limits payload capabilities and robustness to external disturbances, constraining their applications and hindering reliable performance. In this study, we propose a weaving-inspired grasping mechanism that substantially increases payload capacity while maintaining the use of soft and flexible materials. Drawing from weaving principles, we designed a flexible continuum structure featuring multiple closed-loop strips and employing a kirigami-inspired approach to enable the instantaneous and reversible creation of a woven configuration. The mechanical stability of the woven configuration offers exceptional loading capacity, while the softness of the gripper material ensures safe and adaptive interactions with objects. Experimental results show that the 130 g & BULL;f gripper can support up to 100 kg & BULL;f. Outperforming competitors in similar weight and softness domains, this breakthrough, enabled by the weaving principle, will broaden the scope of gripper applications to previously inaccessible or barely accessible fields, such as agriculture and logistics. Song et al. use the weaving principle to overcome load capacity limitations in soft grippers. The woven structure enables exceptional load capacity, supporting up to 100 kg & BULL;f with a 130 g & BULL;f gripper, while also offering adaptive interactions with objects.