I tend to be an all or nothing kind of gal, and for some reason I get the feeling that you're the same way.
SO, I'm going to go out on a limb here and say that instead of cutting out one thing a week, what seems to be working for me is smaller portions. Instead of the big bag of chips I'll get the small bag. Instead of the big bag of m&ms, I'll get the small bag. I don't let myself have 2nd helpings at meals. If I'm still feeling hungry in an hour I'll have a small snack.
I'm an emotional eater, but I'm slowly (very slowly) realising that the smaller portion "fills that need" (I put it in quotations because I'm trying to stop thinking of it that way) just as well, if not better than, the bigger portion. I don't end up hating myself quite as much when I eat the whole small bag as much as I do when I eat the whole big bag.
This may not work for you, but give it a try... I can't cut out things completely, I like my m&m's too much