Snoring can be caused by other factors than being overweight.
Enlarged adenoids, or a floppy soft palate are 2.
If you see an ear, nose, and throat doctor both can be addressed.
Enlarged adenoids are taken out and there is a spray that you can get for the soft palate situation.
Make sure your neck is extended and your chin is up when sleeping..
Sometimes a pillow tips your chin to your chest  which collapses the airway.
Your jaw could be mispositioned often caused by muscle tension.