You have to get your energy from somewhere. Your body needs to keep the lights on, so to speak. The scale may not be a very good indicator of what may be going on. If you’re in ketosis, and it sounds like you are, you should definitely be burning fat. It’s not a huge amount but it’s the most readily available source of fuel and with your history, your body does know how to use that fat for fuel. It won’t be a huge amount. I’m thinking you may use something like 1/4 pound to maybe 1/2 pound per day, I forget where I heard that, it could be off a little. Your water intake, coffee, tea, and anything else you would be taking in with it (salt, other minerals, etc.) will be massive in weight compared to the fat your burning and just one extra half glass of water would probably weigh more than the fat you’ve burned all day.
I tend not to drink as much water when I fast but some may drink more. Adding salt to the water might change how much or little water retention is happening. Also, when I stop the supply of food going in, that tends to stop the exit from the other end… nothing in, nothing out, at least on short 1-day type fasts. Longer ones will usually see things “clearing” in a couple of days, but if it hasn’t cleared, it’s still showing up on the scale.
That’s just my take. Trying to see meaningful numbers on a scale seems like it would be awfully frustrating and probably not all that accurate an indication of what’s really going on anyway.
Don’t think I’m trying to discourage you from fasting. There are certainly reasons why fasting might be considered a good thing, just ask Dr. Fung. But there are limits on just how much fat a person can burn through while fasting, and they may vary somewhat from person to person.
One thing about it, you save on the food budget! 
Hang in there. Make good health the top goal. And it’s OK if it takes a while to reach those weight loss goals. Faster is not usually better. Relax and don’t stress over slow progress or even a plateau. I think we’ve all been there. No matter what it is… “This too shall pass.”