A tensioning system for restricting the available volume of a gastric cavity includes a base material that is shaped and dimensioned for surgical attachment to surfaces on or within the body. Multiple tensioning members are incorporated into the base material, each of the tensioning members including a first end and a second end, wherein pulling upon the tensioning member will cause edges of the base material to be drawn together. The method for restricting the available volume of a gastric cavity includes securing edges of a tensioning system to the gastric cavity and drawing the edges of the tissue together to create a fold in the tissue.