Non-kinking self-wrapping woven sleeve and method of construction thereof

1. A wrappable textile sleeve, comprising:

an elongate wall extending along a longitudinal axis between opposite ends with lengthwise extending edges extending along said longitudinal axis between said opposite ends, said wall being woven from at least one lengthwise extending warp yarn and a plurality of circumferentially extending weft yarns, said weft yarns forming a plurality of discrete annular bands, each of said bands being formed including a plurality of said weft yarns, with adjacent bands being formed with weft yarns of different diameters from one another, wherein said adjacent bands are formed with weft yarns having a diameter ratio of about 1:3.

2. The wrappable textile sleeve of claim 1 wherein alternating bands are spaced from one another by intervening bands, said alternating bands having weft yarns with substantially the same diameter as one another and said intervening bands having weft yarns of a different diameter from said alternating bands.

3. The wrappable textile sleeve of claim 2 wherein said alternating bands are formed entirely from weft yarns having a larger diameter relative to said weft yarns forming said intervening bands.

4. The wrappable textile sleeve of claim 1 wherein said weft yarns are monofilaments and said at least one warp yarn is a multifilament.

5. The wrappable textile sleeve of claim 1 wherein said wall is woven in a plain weave.

6. The wrappable textile sleeve of claim 1 further comprising an outer layer bonded to an outer surface of said wall.

7. The wrappable textile sleeve of claim 6 wherein said outer layer is foil.

8. The wrappable textile sleeve of claim 1 wherein at least some of said weft yarns are heat-set to bias said opposite edges into overlapping relation with one another.