My suggestion would be to allow multiple files to be dragged and shown in the listbox. If you did not clear the listbox either, any newly dropped files would be appended rather than replacing the existing content. Or you could keep a separate list of historic dropped files.
Either way, rather than adding a button to clutter the interface, why not just use the listbox selection change to update display of the file size? The selected file can be changed either by clicking on a listbox item, or by using the keyboard arrow keys.
See the attached project for one way to do this.