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How much Valyrian steel is there that is unused for link making and why aren't people making weapons out of it?

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How much Valyrian steel is there that is unused and why aren't people making weapons out of it?

I was reading an answer by Valorum that stated Maesters can have Valyrian steel links:

Valyrian Steel links (for the study of Magic + the Occult) are exceedingly rare and held by less than one Maester in a hundred. Ironically, they aren't seen as especially prestigious but rather viewed with suspicion.

This made me wonder how much Valyrian steel there is lying around for Maesters to be adding them to their chains. It seems like such a rare and valuable resource like this would be used for crafting weapons not being kept as ingots ready for Maesters to make links.

Indeed the Wiki I linked above claims:

the amount of Valyrian steel in the world is finite and extremely rare

How much of his extremely rare resource is being kept in reserve for link making and why hasn't it been used for more useful stuff like making weapons?