If you are already "spent" at the end of your workout week, adding another day may actually impede your progress even more by using up your energy and taking away even more of your recovery time. For strength workouts especially, it's important to have rest and recovery.
I currently workout 6-7 days a week, but one of those days is yoga (strength, flexibility and balance work) and another is stretch. When I feel like I need a break, I take a day off, or add another stretch day.
What type of weight work do you do? If they are full-body workouts, you might want to consider a split workout instead. I'm doing P90X, and it is a three-day split (like PS or Slow and heavy). I do each workout only once a week, and it's enough for good progress. Yoga also works as a mild strength workout as well.
Another idea is to do 2 days of weights per week (full body workouts, with 2-3 days in between, and add an extra cardio day iin place of the third weight workout.
Whatever you decide, really put as much intensity as you can into the weight work, and get enough rest and sleep and good nutrition to repair and build muscle (which will help burn calories).