A wrappable textile sleeve and method of construction thereof is provided. The wrappable textile sleeve includes an elongate wall extending along a longitudinal axis between opposite ends with lengthwise extending edges extending parallel or substantially parallel with the longitudinal axis between the opposite ends. The wall is woven from lengthwise extending warp yarns and circumferentially extending weft yarns. The weft yarns form a plurality of discrete annular bands, with adjacent bands having weft yarns of different diameters to provide the wall with discrete enhanced hoop strength regions and with discrete enhanced flexibility regions, where the enhanced hoop strength and enhanced flexibility regions alternate in adjacent relation with one another.