There are lots of factors that cause obstructive breathing, even enlarged tonsils. Obesity is correlated to sleep apnea but is not directly associated with it. Many skinny people snore.
Mouth devices might work but most of the time they Don't work. Surgery does NOT work most of the time. However, after surgery you can use lower pressures in your CPAP machine.
I do this stuff for a living, believe it or not hehe..