This is quite the a strange issue as I've adjusted the filter to show the dates between today and the last 7 days . See Screenshot.
Secondly I enabled the debug data for the view so that I can inspect the sql query being passed to the database and what is the number of posts being returned.
As you can see from the screenshots the SQL query is correct and the number of posts to be returned is also correct.
So there might be a plugin conflict somewhere that is overwriting our view display. I would suggest temporarily disabling the non-toolset plugins and trying again.
Also please try remaking this view completely and adding the same filters as in my screenshot and let me know the results as this view could be corrupt as well.
So I created a new View, since this might be bugged and I put underneath the other one for comparison and it still showing everyone, here is a screenshot: hidden link and here is the setting screenshot: hidden link
Also everytime I view the page, there is a new window that pops up with view debugging information, how do I turn it off?
Since creating a new view didn't resolve the issue.
I would like if you temporarily deactivate all the non-toolset plugins to ensure that this isn't being caused by a plugin conflict.
The reason is that from the screenshots in the debug data you can see the sql query is correct as well as the number of items returned is correct but the view is listing out everything.
Once you have done this please let me know.
The debug information can be turned off by going to Toolset -> Settings -> Frontend and scroll to the views debug section.
Ok so I figured that the between weeks filter is not inclusive. This means that if you have posts published in Week 1, 2 , 3 ,4 and you created a query for Between week 1 and week 4. You will only get posts published in week 2 and 3.
However I've added a filter that is explicit to the days hidden link
This should work perfectly for your case as it displays posts that were created today and up to 7 days ago. If you look at the filter on the view you will see what i've done.