No more space in root filesystem, how could I increase the size?

The / filesystem may be a particular challenge, as that needs to be supported by the boot loader.

This answer doesn't specify how to accomplish the requested task, but does provide a workaround.

Another option: find a sub-directory (e.g., /big/) which has lots of data. Then copy that data onto your 60GB of space, mv the directory with lots of space (e.g., mv /big /bigback), and mount your 60GB (or a portion of it) onto /big. After confirming everything works as expected, rm /bigback to re-gain space on /