A woven sleeve for routing and protecting an elongate member includes a wall having opposite edges extending lengthwise in generally parallel relation with a longitudinal central axis between opposite ends. The wall includes warp yarns extending lengthwise between the opposite ends and weft yarns extending circumferentially about the longitudinal central axis. At least some of the weft yarns are provided as bi-component yarns having a central core of heat-set material that biases the opposite edges into overlapping relation with one another, with an outer sheath encircling the central core. The central core and the outer sheath are different colors from one another, such that upon a portion of the outer sheath being split or worn, the central core becomes discernably visible.