I've seen advice here for resizing, which is fine if you have another linux distribution to work with.
How can I do resize the partition otherwise? Are there any Windows tools for example?
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You can then use
resize2fs as described in the linked wiki page.
I have not been able to resize the image on the SD card directly under Windows, however you can back up the linux partition to a file (as described in another question), run
resize2fs on the file, then restore the enlarged partition from the file back to the partition on the SD card.