I don't think there is a way for this as I have this problem myself. It's hard to keep up with it sometimes, as you find lots of good songs and have only 7 days to listen to them properly. Here's a suggestion. Every Monday when you get your new Weekly Discover. Add all the songs from it to another playlist named such as Weekly Discover. Now you dont have to worry about running out of time to listen to all of them. And the best part is. The ones you don't like. Since you added them to a playlist you've created. You can delete any song you don't like at that time. And you won't be confused to which song you've listened to already. It will narrow them all down to which ones you really like. This is what I personally do.
Sadly there is not currently a way to go back to previous Discover Weekly playlists. Many Spotify users have been using this handy little site called IFTTT, and a recipe called Discover Weekly Archive is rather good at saving Discover weekly songs to a personally created playlist of your choice, users who wish to back up the songs from DW week by week: https://ifttt.com/recipes/311873-discover-weekly-archive