It was only around the two month mark of sobriety that I started to lose weight and see changes in my body, and I was exercising every day, both weight training and cardio. I have no evidence for it, but I feel like it took that long for my liver to heal and start functioning properly. I say that only because the difference before and after the 2 month point was quite stark to me - since that point in time, my body has reacted to changes in diet and exercise quite noticeably.
But every person is different, it goes without saying.
I certainly don't think you should expect to gain more weight in sobriety if you're eating healthily and exercising.