Was wondering the same thing and found this question. I ended up finding out how to do it so I figured I'd post it here. These instructions are for when the notebook is stored in OneDrive.
Log into the OneNote app for Windows 10 and right click on your notebook's name. In the dropdown menu that shows up, there should be an option to copy the link to the notebook.
Paste this into a browser to open it up, but pay attention to the end of the link. For mine, the end looked like this.
That miniature link at the end of the full link gave a hint to where the Notebook was being stored, and clued me in to where to look in the next steps.
When you paste the full link from OneNote into the browser, the web version of OneNote will open.
Just under the purple header bar at the top left corner there will be some breadcrumbs. In my case, it displayed as Onedrive -> Documents.
Click the link all the way to the right, which in my case was Documents but may change based on where your notebook is stored. This will open OneDrive in that directory.
Once OneDrive was open in the directory, I was able to find a file icon for the OneNote notebook. If you right click on that, there will be a dropdown menu and the very bottom option should be Details. Select that, and you will be able to see the size of the notebook.
There might be a way to do this that is less of a pain, but I looked around for a while and didn't find an obvious one. Interesting note, if you try and get to the directory mentioned above from the desktop app, all you can see is a web shortcut to open the notebook. The shortcut is only a KB or so, so obviously not the actual size of the notebook.