A bottle of fizzy cola is heavier.
Weight is related to mass. Whenever something loses material and doesn't gain any to replace it, it loses mass. The bottle of fizzy cola has everything the bottle of flat cola has, but the bottle of flat cola has lost some carbon dioxide.
Although carbon dioxide is a gas, and doesn't weigh much more than air, the carbon dioxide in cola is compressed and dissolved and is at a higher pressure and density than carbon dioxide at normal atmospheric pressure. Therefore there is a greater mass of it present. However, the difference in weight would still not be great between the fizzy cola and the flat cola, and it would be difficult to detect.
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