Dear acidrefluxman -
I would worry about the cause of the reflux and keeping the acid under control before worrying about cancer. It takes acid damage to the esophagus a long time before anything happens. I've had controled (mostly non-acid) reflux for over 25 years and don't have damage.
You need to ask why you are refluxing. Do you just have a bad LES valve, a bad hiatal hernia, or maybe you have something like a food allergy that triggers the reflux. Your doctor can look at the first two on endoscopy or barium swallow. You can keep a food journal to find out the last one.
I just ate some yogurt and am now refluxing like mad. It was fine until I ate the 3rd cup. Then I hit my tolerance for sulfites from the strawberry flavoring. I know better too! But at least it's not acid because of Nexium. Uncomfortable, but not causing burn.