The heaviest thing in my kit that isn't specifically listed or implied as something Strider carried is my tarp. 6 lbs of waxed canvas...good lord, it's a bear. But what's to be done? Shelter is essential in the wild. Leave it at home, and that's inevitably when an unseasonable thunderstorm brews up out of nowhere in the middle of the night and the local news runs a story along the lines of "Local Man in Game of Thrones Costume Dies of Authentic Medieval Hypothermia, Corpse Defiled by Weasels, Details After the Traffic".
If only there was a cloth, attested in Middle earth (and preferably Eriador), that could be waterproofed like oilskin but was lightweight like nylon. Preferably something with real-world historical antecedents.
Something like...oiled silk.
When the idea struck me, I wasn't sure if it had ever existed, and researching it is surprisingly difficult. From what I can tell, its history is rather recent in the West--this book from the 1840s discusses it and shows a rather fine hood and mantle pattern.
This mentions it as,
Thin silk saturated with boiled oil, semi-transparent and waterproof. It is much used in tailoring and dressmaking to prevent perspiration from passing through, as at the armpits of garments and the lining of men's hats and ladies' bonnets.
I have no idea where this description originates, but the idea of using it to keep moisture in is a truly horrific twist. One assumes the "boiled oil" in question is linseed oil, though that's conjecture.
In Camping and Woodcraft (1906), Horace Kephart refers several times to waterproofed silk tents, "sheltercloths", and even provision bags. However, at one point he refers specifically to the fabric of a tent as 'balloon silk', which to my understanding may have meant a very fine silk-like weave of cotton, rather than actual silk. This throws into question whether the 'silk' he referred to in other instances was animal or vegetable in origin.
I can't find any mentions before the nineteenth century in Europe, though China (as one would expect) developed such things as well--this page says they used tung oil, though during which time-period is unspecified. This page says the Chinese had oiled-silk umbrellas "over 1,000 years ago".
All that said, if one has waterproofing oils and one has silk, the combination of the two seems intuitive. So...who had silk?
Two persons we know of actually possessed it: Bilbo (at the beginning of Fellowship) had an embroidered waistcoat, and Elrond (at the end of The Hobbit) gave Bilbo a red silk handkerchief to replace the articles he lost over the course of his journey with the dwarves.
Gandalf also mentions silks alongside linens at the end of Return in a way that implies both are cloths of surpassing fineness.
All other mentions of silk in the books reference the "silky" nature of the hithlain cloth and rope of the Galadhrim, or the spider silk spun by Shelob.
So, did the Dunedain have access to silk, and if they did, would they use it for tarps?
I think the question of access is one of conjecture. The origins of silk in the Shire and Rivendell are unknown. The nature of the Shire as an analogue of pastoral England makes me think it's imported, though I could envision the Noldor of Rivendell producing it domestically. It is very clearly viewed as a luxury good, though its use in handkerchiefs implies that it wasn't so rare that it couldn't be put to utilitarian purposes...albeit by the very wealthy. (Is Elrond wealthy? He obviously commands a lot of resources, but I've always sort of viewed the elves--in Rivendell and Lothlorien, at least--as operating on a sort of Star Trek post-scarcity communist system.)
The fact that Gandalf mentions it alongside linen, extolling the fineness of both, may imply something or nothing. Linen is elsewhere mentioned as being used for bedding in Rivendell, as an analogy for the suppleness of mithril chain...and as one of the contents of Sam's pack, and serving as a bandage for Gimli's head. Clearly linen comes in various grades. The same is likely true of silk, but almost certainly to a lesser degree.
I must say, if I were a ranger and had access to silk, through my contacts among the elves, dwarven traders passing through the Shire and Bree, or otherwise...a waterproof tarp would be my first priority. It could be worn as a poncho or over-cloak, used as a tent (though certainly not a groundcloth like canvas is) and could keep anything wrapped in it dry when not being worn. It would take more weight off of the kit than any other single change I can think of, and serves arguably the most indispensable role in that kit.
Another interesting note regarding grommets:
While looking through mentions of silken shelters in Kepharts' book, I noticed that he had some interesting things to say about grommets. The two-piece, hardware-store-style grommets are obviously quite modern and not suitable for a really authentic kit. The alternative is the (comparatively delicate) embroidered grommet, or other tie-outs.
Kephart also warns against two-part grommets, but not because of 'authenticity'--rather because he views them as inferior on terms of strength to a steel ring stitched to the surface of the cloth. This seems like a very good, period-appropriate technique which, while likely as labor-intensive as the embroidered grommet, may be superior in strength to modern grommets.