I believe that time lag, as much as bias, is the death knell of the weekly. Used to be, when something hit the headlines, you could expect to get a fuller more complete analysis of the issue in a few days when your Time or Newsweek came in the mail. Now, you can get that same (and better) level of analysis online right now and for free at a multitude of sites, and even on cable if you choose wisely.
With the vaunted "24 hour news cycle" there is no market for week old news. Life has passed these relics by. Too bad, so sad.