Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
A repeating background for websites with a texture of black groove stripes.
Source V. Hartikainen
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
Textured Red Brown Plastic, Free Background Pattern. Although there's already enough plastic in our lives, let's bring it to the web too.)
Source V. Hartikainen
Seamless SVG vector and JPG backgrounds with faded diagonal stripes. The colors are editable.
Source V. Hartikainen
Looks like an old wall. I guess that’s it then?
Source Viahorizon
You can never get enough of these tiny pixel patterns with sharp lines.
Source Designova
The rectangular tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Here's a subtle marble-like background for use on websites.
Source V. Hartikainen
Can never have too many knitting patterns, especially as nice as this.
Source Victoria Spahn
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Groovy Concentric Background No Black
Source GDJ
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
This reminds me of Game Cube. A nice light 3D cube pattern.
Source Sander Ottens
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Here's a new background image for websites with a seamless pink texture. It should look beautiful with website themes where light pink background is needed. The background is seamless, therefore it should be used as a tiled background.
Source V. Hartikainen
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
Dark pattern with some nice diagonal stitched lines crossing over.
Source Ashton
Retro Circles Background 8 No Black
Source GDJ
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