Well done for starting to make positive changes. I also suffer from Binge eating disorder. I've managed to overcome it for the first time ever last year and lost 4.5 stone, but in the last couple of months it's come back and I've put half a stone back on. It's like part of my brain is shouting 'what the hell are you doing?!' to the other part while I shovel food into my mouth!
However, I am now back being healthy again. A few things that have helped me:
Realising that our brains are still much as they were when we were cavemen, and if we found a sweet, high calorie food (e.g. a honeycomb) the best thing we could do would be to eat it all. Our bodies would store the food and it would help us get through leaner times. But now, sweet high calorie foods are all around us, and cheap to buy, but our brains still think ' we need to eat all this now, so when there's no food we'll be ok'. Understanding this took some of the shame out of it.
A mantra I say to myself is 'i can have cake any time I like, I'm just choosing not to have any today '. Also 'the shops will always sell xxx, so it's ok not to buy any today'
I find if I completely cut out sugar it's inevitable I will relapse, so I build planned treats into my plans. I can enjoy the food guilt free, because it's not a binge, it's planned, and I don't find that I want more afterwards.
Btw I lost the 4.5 stone without WLIs. Nothing against them, but it is possible to do it without.