Tissue anchors comprise a woven filament braid body having an elongated tubular configuration and a foreshortened configuration where proximal and distal ends of the body expand radially into double-walled flange structures while leaving a cylindrical saddle region therebetween. The tissue anchors are deployed through penetrations between adjacent tissue layers, where the flanges engage the outer surfaces of the tissue layers and the saddle region resides within the tissue penetrations.