There are health benefits of reading beyond just mental health. The average human brain accounts for about 2% of your body weight, but it burns nearly a quarter of your energy. Reading gets your mind working, so it follows that some intensive reading would chew up some calories.
Unfortunately, reading is more of an intellectually active activity instead of physical. Sitting and reading only burns about 50 calories per hour. Meaning that it would take quite a while to lose any weight while just reading.
However, there are plenty of people who read while doing other exercises—listening to an audio book during their morning jog or flipping through pages while walking (slowly) on the treadmill. This works your body and mind simultaneously.