There are times when we want to add a site as a new network place and browse our way around. The best way of doing this it to add the following URL in network place wizard: -
make sure you add default.aspx to the site name otherwise the site will be added as a normal folder (as in open in explorer view mode of SharePoint UI) and not in webfolder format.
Site added as a web folder.
Site added as a normal folder.