When you use File > Place, make sure you click on the Link button at the bottom of the window.
Illustrator files can get very large, even when working with linked images. If you saved your file using the default options, you left Create PDF Compatible File on. This makes Illustrator save an embedded high resolution PDF of your file, and PDFs can only contain embedded images. You cannot edit the PDF portion of the file, it is used to provide cross-application compatibility with InDesign, Photoshop, Acrobat, or other programs that can read PDF but not Illustrator’s proprietary file format. If you are placing many high resolution images, you are going to see your file get quite large, even though the images re linked, at least as far as the editable Illustrator portion of the file is concerned.
If you do not intend to access the Illustrator file using any program except Illustrator, you can save considerable space by turning the Create PDF Compatible File option off when you Save or Save As. I have seen files drop from over 200 MB to under 1 MB.