I can speak from experience. I wound up at the Mayo Clinic in Rochester, MN for a week and after a weeks worth of tests for other symptoms the doctor wanted to put me through a sleep study. Long story short, the study showed that I had pretty bad obstructive sleep apnea. On average 26 times per hour I would stop breathing for 19 seconds per episode. Obviously this grounded me instantly. Make sure before you get tested, if you decide to, that you talk it over with your AME. Once diagnosed with sleep apnea, the examiner is forced to report the findings to the FAA. The FAA has certain tolerances for Apnea as far as treatment being needed and what's acceptable. Weight loss alone is not enough treatment for the FAA. I wound up having surgery to get my tonsils out along with septoplasty on my nose to remove some bone spurs and straightening of my septum. After the worst surgery of my life I was required to wait at least a month( 2months recommended) before a follow up sleep study is required to see the benifit. Yes, that was all done in one surgery. With the surgery and use of a CPAP machine as treatment, the FAA said that my post surgery apnea was within workable tolerance provided that I did a MWT(maintenence of Wakefulness Test) once a year for 3 years to prove that I was actually getting sound sleep at night. The MWT is about the most boring thing you will ever do. You show up at the sleep clinic at 6:00 am. They hook you up with wires and machines and then you sit on a bed in a dark room for 30 to 40 minutes and you are told not to go to sleep. You have to just sit there and sit still. After your first session then you go out into a waiting area, or in a bedroom similar to a hotel room for 2 hours before your next dark sit. You do this dark sit for four times repeated every 2 hours and then you are done. The key is to prove that you are getting enough sleep at night that you don't fall asleep during the day. The test sucks, but if you really want to fly at this point you will make sure you don't fall asleep. After 3 years the FAA finally sent me a letter saying that I was no longer required to take this test. I didn't require a special issuance medical anymore, with the honor system in place that I will consult my AME if I notice the apnea resurface as a problem.
I know this all sounds scary to any pilot for fear of losing a medical for a while. For me though it was a no brainer. Sleep apnea CAN KILL YOU. I would rather be alive without a medical than dead because I was stubborn.
Many doctors will tell you that lots of overweight people have sleep apnea, however they don't know it because they haven't had a reason to get tested. Usually a spouse will complain that they can't sleep because of your snoring, or you just don't feel rested in the morning will lead you to look further.
Good luck with your decision and remember to consult a pilot friendly AME before proceding with any procedures or tests. PM me and I can give you my AME's contact info if you have questions. He is very well versed on the topic and has worked many cases with the FAA military and civilian.