If you’re looking for an ultra-minimalist wallet this single-sheet-as-wallet paper folding trick should do the trick.
Instructables user Hunter Frerich shares a simple tutorial demonstrating how you can fold a standard piece of printer paper into a lightweight and minimal paper wallet. The results are impressive and, according to him and the commentors on the tutorial, quite durable. If you’re looking for something with the thinness and lightness of the paper wallet with a bit more durability, you may want to check out the incredibly light All-ett (I’ve had one for years and it is my favorite wallet by far).
Paper Wallet [Instructables]