One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
Light and tiny, just the way you like it.
Source Rohit Arun Rao
Remixed from a drawing in 'Incidents on a Journey through Nubia to Darfoor', F. Ensor, 1891.
Source Firkin
Prismatic Abstract Geometric Background 4 No Black
Source GDJ
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Derived from an image that was uploaded to Pixabay by mdmelo.
Source Firkin
Abstract Tiled Background Extended 10
Source GDJ
Prismatic Groovy Concentric Background No Black
Source GDJ
Dark blue concrete wall with some small dust spots.
Source Atle Mo
A beautiful dark padded pattern, like an old classic sofa.
Source Chris Baldie
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Medium gray pattern with small strokes to give a weave effect.
Source Catherine
This was formed by distorting an image of a background on Pixabay.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
You know I love paper patterns. Here is one from Stephen. Say thank you!
Source Stephen Gilbert
Same classic 45-degree pattern, dark version.
Source Luke McDonald
Prismatic Snowflakes Pattern 3 No Background
Source GDJ
Inspired by a drawing in 'Kulturgeschichte', Freidrich Hellwald, 1896.
Source Firkin
More in the paper realm, this time with fibers.
Source Jorge Fuentes
This background image has seamless texture that resembles a surface of gray stone.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A simple circle. That’s all it takes. This one is even transparent, for those who like that.
Source Saqib
Fake or not, it’s quite luxurious.
Source Factorio.us Collective
Remixed from a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
I skipped number 3, because it wasn’t all that great. Sorry.
Source Dima Shiper