Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Abstract Geometric Background 2 No Black
Source GDJ
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
A background pattern with a look of rough fabric.
Source V. Hartikainen
Seamless , tileable CC-0 texture. Created by my own, feel free to use wherever you want!
Source Linolafett
Seamless Dark Grunge Texture. Here's a new grunge texture for use as a background.
Source V. Hartikainen
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
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
Number 3 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin
Looks a bit like concrete with subtle specks spread around the pattern.
Source Mladjan Antic
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
Prismatic Curved Diamond Pattern 7 No Background
Source GDJ
An alternative colour scheme for the original seamless texture formed from an image on Pixabay.
Source Firkin
Not the Rebel alliance, but a dark textured pattern.
Source Hendrik Lammers
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
These dots are already worn for you, so you don’t have to.
Source Matt McDaniel
Real snow that tiles, not easy. This is not perfect, but an attempt.
Source Atle Mo
There are quite a few grid patterns, but this one is a super tiny grid with some dust for good measure.
Source Dominik Kiss
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
A dark striped seamless pattern suitable for use as a background on websites.
Source V. Hartikainen