Would I gain weight eating a can of tuna everyday?

No single food item will cause weight gain or loss.  If you eat a 5-ounce can of turn in oil, you're probably eating 100 calories.  That's not that much.  IF you need to decrease your consumption of something else to compensate for 100 extra calories, then that's what you do.

BTW, sunflower oil really isn't that heathy.  

have the tuna in water

Tuna is a source of mercury, you should avoid eating it daily, especially higher-mercury varieties like albacore tuna. But if you wish to do it, depending on what else you eat, it alone will not cause weight gain.

Best wishes