I have what is considered good insurance, and it cost me $750 out of pocket for a sleep study. So hope you've got the cash.
The good news is I got a CPAP machine and couldn't be happier, now about a year in. My only advise is don't cheap out just get the top model with the features, e.g. you want autoset pressure, not static, the heated hose, and play around to find a comfortable mask. Now I stop breathing something like 0.3 times per hour which is apparently "amazing" you can still have up to 5 times per hour and be considered "OK". Also shop around as the place that tested me, kept trying to convince me to go with a static pressure model to "save money" even after making it clear I wasn't interested in that.. but I purchased my machine from perthcpap.com.au instead and the autoset model cost less than they wanted to sell me the static for. Go figure.
I had a few people I know who didn't tolerate it so well and most of them got non-autoset and non-heated and it makes a huge difference. The mask you use also matters a lot.
The difference to my alertness, how I feel after sleeping, and not getting super tired and needing a nap in afternoons is incredible.
TL;DR: Get a sleepstudy. At least here it's a home test where you just where a machine and a few sensors and takes 1 night.
So this isn't an either/or situation. Sleep apnea can also be a contributing factor in being overweight. So do everything: take steps to eat better, sleep better, and exercise more. Small steps in a number of areas are often better than a big step in just a single area.
My dad has had 30+ years since he was diagnosed and his apnea symptoms are terrible and really noticeable.