How do I resize a Linux filesystem data .bin file?

We will try to make your two MB root.bin file to a 12 MB to demonstrate the steps.

Create a copy of your file (just in case for backup purpose):

cp root.bin 12mb.bin

Run this command to add 10M to the file size:

dd if=/dev/zero of=12mb.bin bs=1MiB count=10 conv=notrunc oflag=append

Now 12mb.bin is not 2M any more, actually its size is 12M.

Run:

e2fsck -f 12mb.bin

to check the filesystem on the file, then run:

resize2fs 12mb.bin

Done. mount it somewhere:

sudo mount 12mb.bin /mnt

check the size:

df -h --output=size /mnt/
Size
 12M

And the existence of files:

ls /mnt

We can also use losetup to act with the file like a block device:

sudo losetup -f 12mb.bin

then:

sudo losetup -l | grep -i "12mb.bin" | awk '{print $1}'
/dev/loop0

and we can resize /dev/loop0.