Soft grippers have excellent adaptability for a variety of objects and tasks. Jamming-based variable stiffness materials can further increase soft grippers' gripping force and capacity. Previous universal grippers enabled by granular jamming have shown great capability of handling objects with various shapes and weight. However, they require a large pushing force on the object during gripping, which is not suitable for very soft or free-hanging objects. In this paper, we create a novel palm-shape anthropomorphic variable-stiffness gripper enabled by jamming of 3D printed fabrics. This gripper is conformable and gentle to objects with different shapes, requires little pushing force, and increases gripping strength only when necessary. We present the design, fabrication and performance of this gripper and tested its conformability and gripping capacity. Our design utilizes soft pneumatic actuators to drive two wide palms to enclose objects, thanks to the excellent conformability of the structured fabrics. While the pinch force is low, the palm can significantly increase stiffness to lift heavy objects with a maximum gripping force of $17\,$N and grip-to-pinch force ratio of $42$. We also explore different variable-stiffness materials in the gripper, including sheets for layer jamming, to compare their performances. We conduct gripping tests on standard objects and daily items to show the great capacity of our gripper design.