Why is weight gain a symptom of Cushing's Syndrome?
Cortisol is released when body goes through stress situations like while working out in gym, physiological activities outdoor etc. As you have already mentioned about what Cortisol does, it accumulates in the body after the stress situation and then with the intake of food and other nutrients it replaces the consumed carbohydrate and fat in the body i.e. a kind refueling. So this is how Cortisol maintains the body weight normally if our body gets enough exercise or has proper metabolism.

Whereas in Cushing' syndrome which comes usually by taking glucocorticoid drugs, or diseases that result in excess cortisol, adrenocorticotropic hormone (ACTH), or CRH levels. In this case Cortisol content will be more than the normal level which in turn requires more carbohydrate. So cortisol metabolizes the food and reefuels the body even when there is no requirement within the body. So because of excessive cortisol content body simply gets excessive fat accumulated in various parts which mainly results in obesity.

One more explanation from High level of Cortisol effects:

Chronically high levels of cortisol plays a big role in the development of obesity.



  Cortisol helps the body handle stress; so, when stress goes up,
  cortisol also goes up. Cortisol stimulates fat and carbohydrate
  metabolism during stressful situations. This leads to increased blood
  sugar levels required for fast energy. In turn, this stimulates
  insulin release which can lead to an increase in appetite.


  Adrenaline increases alertness and metabolism by helping fat cells release
  energy. When the immediate stress is over, the adrenaline levels
  return to normal. But, cortisol lingers to help bring the body back
  into balance after stress. One of the ways it gets things back to
  balance is by increasing appetite to replace the carbohydrate and fat
  used for the flight or fight response.




  The problem is that in today's society, stress-causing situations do
  not really require the body to use up a lot of energy. So, cortisol
  ends up causing the body to refuel after stress even when it doesn't
  really need to refuel. This excess fuel or glucose is converted into
  fat resulting in increased storage of fat.