For a long time now, my husband wakes up with this burning sensation in his stomach but he is afraid of cancer.

Seek evaluation: Although a diagnosis of cancer can be scary and anxiety producing it is better to know what is happening rather then let it persist. I would recommend strongly that your husband speak with his primary physician and if needed proceed with a GI consultation for possible endoscopy. Remember it is not always cancer, it could also be an ulcer. Both can be threatening.

Fear in Medicine: I think it is very normal for humans to be afraid when it comes to the unknown about their bodies. But, given his age, this is almost more likely to be an ulcer and not cancer. There can be a blood test for the ulcer and he may not need a scoping yet. Please encourage him to get to his family doctor for this simple blood test and treatment that may very well make him feel better.