Maybe she's growing more at the weekends when she's resting? Extra sleep = growth. Or maybe the food there is saltier and she's retaining water more.

I too am worried about the regular and obsessive weighing. It's actually normal for teenagers to grow and get heavier. Or maybe there are some really unhealthy food choices at Dad's and she's bingeing there because she can. I would eat/overeat secretly if my mother was weighing me all the time and on my back about healthy food all the time.

If she is actually overweight or gaining weight very fast it could be a good idea to see a dr and get an assessment and a referral to someone who will provide some psychological support along with diet/exercise measures. I'm much more concerned about the unhealthy psychology/potentially disordered eating that's going on than the weight gain. But I think maybe you need some help and support looking at the total picture to get the best possible health outcomes for your DD.