We gave him some money, sure, but most of it went up his nose so we stopped.

That guy this is referred to is a pillhead, so I assume it just means that he used to buy drugs for the money they gave him, but maybe it's some idiom the meaning of which is unknown to me, and it means something else?

Yes, he spent it on drugs. Cocaine, for example, is often inhaled up one's nose.

You are correct. It means he used the money to buy drugs.
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