So in short:
Nylon should be considered for a tailoring option and material.
Rare to some degree in tailoring so it would not show up all that often. You can find full garments and materials in only a few locations.
Shirts/Pants/Shorts/Coats in sports, fishing and camping shops. Typically these garments are very expensive and that adds to the rarity reason. $65-95 for a shirt and pants are (oddly enough less rare) $35-75(not fishing waders either, normal garments).
Arts & craft stores sell 100% nylon, sometimes called "Rip-Stop Nylon".
-Cool(so not warmth friendly)
-Quick drying and NOT absorbent
-Water resistant to reduce "Wet" morale debuff
-Damage resistant even as 1 layer which is paper thin
Upgrading using nylon "Rags"/"Sheets" or however you wish to define it in function should give almost no encumbrance at all. 1-2 at the most. If you have even seen such material first hand, you will notice it is by design not to be bulky and yet still have all of these qualities.
A rare in game fabric, more so than kevlar. It would be the the lightweight answer to upgrades, assuming leather is going to remain "thick".
Examples of full garb and upgrades:
-Socks(fits) 100% nylon would give better buffs than standard fabric socks ; upgrading with nylon would be no added encumbrance even over nylon garments, due to how thin the fabric is while retaining the good qualities.
The only way an encumbrance would be noticed would be for like, 4-5 layers and used specifically as a garment made as Armor. Standard shirt/pants/gloves etc would be just "better" versions or whatever garment made of cotton.
So...ok, why at all?
I hate with a passion not having a light weight option as "armor" while still being able to not consider what my character wears as "armor" specifically. What I wear for camping and hiking is not armor. Looks, feels and seems like normal clothing in every respect. But it does in fact bear such qualities. Great stuff...just friggin expensive and hard to find in every day normal shops >_>