obstructive sleep apnoea is well known in obese people...
it doesn't "treat" the problem, it just relieve the symptoms so that u can maintain good oxygen saturation when you're sleeping.

lots of people with OSA tends to have lower blood oxygen saturation because of upper airway obstruction, by giving positive pressure, it helps to pump oxygen into the lungs.

ultimately, losing weight...lots of weight is the best remedy to this problem..

nope, the effect is not placebo, one can feel drowsy and sleepy due to the carbon dioxide retention in body when you have obstructive sleep apnoea,
you'll have lower blood oxygen saturation to start with.

The machine helps to relief all these symptoms by making sure you have good oxygen saturation in blood. that's why you feel fresh the next day when you wake up.

i do come across lots of these cases...but i'm not the patient.
depends on the severity of disease, if you're young , you should start off with diet and lifestyle changes because that helps a lot.
Sleep position sometimes can affect the patency of airway when you sleep.

when nothing above works, surgical indication like removing part of your palate sometimes help.