John has a BMI of 35 and is desperate to get it down to at least 25. He is trying a low-sugar, low-carbohydrate diet. John is likely to have difficulty losing weight while dieting because:

Because fat tissue require lower energy for maintaining them than body muscles.

Explanation:

In the Question it can be seen that john is highly obese as his body mass index (BMI) indicates. So most of his body mass is composed of fats and fats require smaller energy for their maintenance.

Many researches on obesity indicates that people don't lose fat cells by carefully eating. Acording to Kirsty Spalding our body has same number of fat cell which it is programmed to and only the size of fat cells changes. So we can either shrink the fat cells or increase their size. So by cahnging diet plan we could not destroy them.

So, John is facing difficulty in losing weight while consuming the low-sugar diet because most of his body mass is composed of fats and fats require lower energy for their maintenance.