How do I export whole Unity project with all scenes?

Just save your scene and project and close unity and simply copy the project folder or make an archive of that main project folder and copy it. (Closing Unity is an important step because all temporary files are deleted which were opened)

And about the file size, yes generally they are bigger if you have used high quality models or textures. You can try building it for a platform like Android or Windows etc. and send that executable build to somebody else (usually smaller file size).

P.S: Have tested it before and works like a charm.