How can I construct a lightweight privacy panel 3-4ft high by 8ft long or thereabout?
How about using the systems that are used to hide A/C units? they are 3-4 feet high, attractive in appearance and you can link together as many as you wish. And when you want to take them down they are light and can be easily broken down and stored. They come in white, but with a little PVC paint they can become any color you desire.

Another option would be creating a frame with boards and attaching trellis boards.  With this option you can use hinges and make it fold for easy removal and storage.  You could also add some pretty artificial foliage for extra privacy.