Here is what you can do:
Download the small files and the file structure as an archive (zip or tar). The big files will be included namewise but the data will not be there. To get the content of the big files you need to download them individually from the web interface. This way you can get the file structure but the heavy loads only on demand!
Download the small files as GIN archive(*.gin.zip). This is comparable to the situation above, however, you also get the history of the files and the possibility to request the big files via git-annex or the GIN-client.