" Back in 1916 airplanes were covered in linen and treated to be weather and fire-resistant, unfortunatly I don't know exactly what the treatment process was but it might be worth researching if you need something cheap and light. "
The dope the aircraft fabrics were covered with was not simple, fire resistant or cheap. Was a cellulose/solvent product of some well researched sort. Shrank when it dried to stretch the fabrics taught. Waterproof. Model builders use something similar/more modern to stiffen paper over balsa.
Painters taps work great hung vertically. I used my heavy ones from painter's supply Dunn-Edwards in SW USA to curtain my woodshed. They are I think, a 13?oz canvas. Don't allow moisture through by being dense and heavy, but will breathe. Not super expensive if bought on sale, in fact cheaper than good poly. 8x12 might have been less than 30USD. Would last long enough to be a very good compromise for all things tarp except for maybe construction of roof.
NOT the thin wannabe stuff purchased at Home Depot which is predictably garbage. Had a thin waterproofing layer of plastic bonded to it instead of density, which flaked like millions of fish scales after sun exposure. More expensive than Dunn-Edwards, amazing.
Hand grommeting is simple and cheap with a little purpose made anvil available from General Tool.
Hayfield tarps are not a withering compromise. 12mil poly, silver one side black the other, heavy rope edges and grommets. Last a very, very long time outside here in B.C. 250CAD for a 30x50ft at Princess Auto. We use them black side up to cover fallow gardens 2yrs at a time. Scoop water making snow up off of the smoothed out dirt surface.
I have a number of various treated canvas tarps from Tarps USA. 21oz treated. Expensive but have lasted a few years outside now. Snow/rain cover for heavy equipment and timbers. I am willing to pay for quality, and the heavy canvas reminds me of my dad's back when quality outdoor goods came as a matter of course when purchased from Sears. New 21oz still not as heavy the old remaining Sears tarp I have.
The heavier canvas 18oz.? from Princess Auto, bought on sale has been good fulltime in the weather as well. Color has faded, tarp has softened more than my USA (made in India).
FWIW - the old waxed canvas tarps could be used to filter water from gasoline. Gas would pour through, water was retained. Needed to be rewaxed after.
Canvas tarps can be torn a little more easily than ripstop poly if you are the kind of person who drags tarps across things rather than lifting and folding. You will be sad if you do.
+1 to Carmen Rose for suggesting lumber wrap that would be otherwise landfill bound. Waterproof, reinforced, typically has a few holes, one side black. I have used it as blackout curtain for a greenhouse, and covering of outdoor goods, tarping small patches of garden. Lasts quite awhile, free. Stretches flat easily, lightweight, takes staples.
I have much better luck up here than in Nevada/Arizona. Sun is murder.