You might consider any of the versions of the Japanese tabi sock/boot.

In its simplest and lightest form you get a cotton canvas form-fitted sock that is split to alloy you to slip on sandals over. The tabi socks I used had a double layer of canvas on the bottom and were suitable for padding around the house or airport.

There is also the jika-tabi which is a heavier version of the tabi but with a thinnish, but tough, rubber sole that is intended for outdoor wear. They are apparently quite popular with farmers and many construction workers.

jika-tabi can be anything from a form-fitted slipper suitable for going out to get he morning paper to very heavy units which pretty much have the same protective properties as a heavy work boot.

These are also marketed to westerners as 'ninja boots' and are sold at martial arts schools.

All of these are light weight, and fold into a compact package.