What you did is save an empty library to your external drive. That's why it has hardly any size. There's nothing in it.
Now you need to move your project to the empty library. To do that, go to the projects browser screen (the one that shows your projects as icons). Select the project by clicking once on it and a little circle with dots in it will appear to the right of the title. Click on the circle and a drop down menu will give you the options to move or copy the project to the library that you choose. Both libraries must be open for the options to appear. Otherwise they will be grayed out. The reason is that you cannot move a project to a closed library. So open them both so that their library names appear in the iMovie project sidebar.
Here's an online help link that describes how to copy and move projects between libraries:
https://help.apple.com/imovie/mac/10.1/#/mov3fa25bae7
It is a good idea first to copy, not move, the project to the external drive. Once you are sure that the copied project is functioning properly on the new library you can delete the original one from your old library.
-- Rich