Not even 1kb, but very stylish. Gray thin lines.
Source Struck Axiom
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
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
The square tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i
Source Firkin
Derived from a drawing in 'Historiske Afhandlinger', Adolf Jorgensen, 1898.
Source Firkin
An abstract Background pattern of purple twisty patterns.
Source TikiGiki
A background pattern with a look of rough fabric.
Source V. Hartikainen
Bigger is better, right? So here you have some large carbon fiber.
Source Factorio.us Collective
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
Prismatic Hexagonalism Pattern No Background
Source GDJ
Background Wall, Art Abstract, Block Well & CC0 texture.
Source Ractapopulous
Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
Prismatic Snowflakes Pattern 2 No Background
Source GDJ
Seamless pattern inspired by a drawing on Pixabay. To get the tile this is formed from, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
From a drawing in 'Navigations de Alouys de Cademoste.-La Navigation du Capitaine Pierre Sintre', Alvise da ca da Mosto, 1895.
Source Firkin
Because I love dark patterns, here is Brushed Alum in a dark coating.
Source Tim Ward
Sometimes simple really is what you need, and this could fit you well.
Source Factorio.us Collective
The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.
Source Nathan Spady
I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
ZeroCC tileable mossy (lichen) stone texture, edited from pixabay. CC0
Source Sojan Janso
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin