Many people lose a lot of weight during their first week of LCHF. Motivating, sure. But why?
On a ketonic diet (low carb, high fat), just like any other diet, the body will initially lose water weight. You can't burn fat in the beginning as it takes time for the body to shift to the new source of energy. What happens is that the body starts using it glycogen reserves. How much glycogen one has is highly individual but usually is around 0.5-1.5 kg. In addition, for each molecule of glycogen you lose, you'll lose 4 molecules of water. Or put differently, for each gram of glycogen, there is 1.7 gram of water.
If you lose your 1 kg glycogen reserves in the first week, you will lose another 1.7 kg of water, adding up to a total of 2.7 kg. This is what the big weight loss in the first week is about.
There is nothing wrong with losing this water. It will make you feel less bloated and your measures decrease. But, if you start eating carbons again, your body go back to producing glycogen and binding water. Cheating could therefore have an extremely deterrent effect. Depending on how many carbons you eat, quick weight gains are very likely. Luckily, as soon as the body runs out of glycogen you will be back to your pre-cheat weight (unless you had so many extra calories you actually gained weight off course).