Tuna bellies are the part of the Tuna that the Japanese like the best and it sells for more than regular lean tuna. It's called Toro in Japanese.. "fatty tuna" Personally I love it and keep it for sushi/sashimi. Tuna when smoked dries out very fast even the fatty parts. It will render out to be hard as a rock if left too long. I cold smoke and hot smoke it. When hot smoked you need to watch it real carefully and pull it off the heat way sooner than you think. It will continue to firm up/dry out as it cools too. It will absorb a wet brine pretty well as long as there is enough sugar/salt in it so that it absorbs it well. This will help it not dry out as fast when hot smoked.
If all else fails the tuna belly is one of the best baits I have every used for crab, prawn, ling cod, halibut etc.. cause of it's high oil/scent trail it produces. I don't use the good parts just the scrap cuttings. Vacuum pack it and use it for bait on it's own or mixed with other stuff.