Some of them have names which don't match up with any used tileset, so I wondered how I could view the data, to see if they contain anything interesting.

Maybe we can look at the code for them in a hex editor.
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Never use a flash drive unless you are transferring files...

It is all meaningless to me. A lot of it is 00s though. No header text.

25 days later... lol

This is the code that reads CHK files.
https://github.com/Dirbaio/NSMB-Editor/blob/master/NSMBe4/NSMBTileset.cs#L388-L394

CHK files are super simple, they're the tile behavior files.
They contain 4 bytes for each Map16 tile. The first 4 bytes are the behavior for Map16 tile 0 (the one at the top left), next 4 are for tile 1 (the one next to the right) and so on for all tiles, in left-to-right, top-to-down order.

There are lots of zeros because there are lots of tiles that have all zeros as their behavior