If you are bringing your phone anyway, might as well use that for your mapping needs?

You can have a backup paper map inked on your skin.

I like to keep my orientering skills sharp, so use a compass and map to navigate. I take my phone with me and it can serve as backup navigation, but I usually just keep it powered off and sealed in a waterproof bag.

I have previously wondered about printed handkerchiefs and bandanas that functioned as backup maps. Invest in my kickstarter!

https://truenorthmapco.com True North makes a great bandana sized map of the BWCA areas.

That's a great idea!

(Mildly amusing, I first read 'printed handkerchiefs and bananas'. Like paint your map on the skin of your apple, or the shell of your hardboiled eggs.)

And then there are things such as maps printed on silk...

... and tyvek (no idea if that wins on weight, but they're disproportionately durable)