There is only one file type that uses the .WEAVELIBRARY extension:
Painter Weave Library
Library created and used by Corel Painter, a drawing application used to create digital artwork; holds a collection of media weaves, which are textured patterns that can be added to the canvas; includes Pastel Plaid, Checkerboard Diamonds, and Picnic weaves; similar to .ABR Photoshop brushes.
The library of weaves can be accessed through Painter's Media Library Panel. Selectand the Media Library panel will appear with tabs for Pattern, Gradient, Nozzle, Look, and Weave libraries. You can then choose to create, import, or export a library with the "weavelibrary" extension.
Updated: July 19, 2019