You won't get ankle support with any shoe/boot under 1kg. So, you will have to choose between the two. Either a light boot/shoe with no support (even if it has the appearance/illusion of support), or heavy boots that actually have ankle support.

Who knows, maybe I am wrong, and there actually is a boot out there that is light weight and actually provides ankle support. I carry an ankle brace just in case I need real support.
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