Could be obstructive sleep apnea, being overweight tends to reduce the size of the throat opening connecting to the lungs and then any fatty tissue can cause problems when one lies on their back and gets very relaxed, sleeping.
At the age of 38 I think this is unlikely.
A sleep study is rather expensive, if you have insurance that pays go for it. A less expensive test is a recording Oximeter run for one night. This can be done at home with equipment delivered and picked up at your door. I had that done first and while I have insurance I did note the low cost with some surprise.
Check if snoring happens only when he is sleeping on his back - ask him to sleep on a side. There bay be some aids one can wear to discourage sleeping on one's back.
there's a lot of suggestions you can get from www.snoringsolutions.info
He needs to talk to his doctor about his snoring, it could be a sign of sleep apnea which does have treatment. If his doctor suspects sleep apnea, he or she will probably order a sleep study test in a facility (usually a hospital sleep lab) that would monitorsyour hubby overnight for periods of apnea, oxygen levels, snoring, any disturbances of the heart rhythm, his brain wave activity etc...
Definitely push him to see his doc...Sunny