Swelling means it's getting bigger. If you see a bulge then I'd worry.
STOP MAKING SENSE.Go to an apple store and compare their models against yours.
To be honest I think you're just thinking too much. If a dodgy battery swells up the chemicals inside are reacting with themselves. The volume expands. There is no additional mass input (conservation of mass) so there's no way it can get any heavier.
Unless it's reacting with oxygen which in that case your battery may probably... er... explode? Even if a dodgy battery does partially react with oxygen you're talking about minuscule amounts.
And even if it swells up it will not change the centre of mass of the iPad through deformation (to a large extent). Really.
What do you mean the bottom feels heavier than the top? It's one solid piece?
everything should be symmetric in relation to the ipad body.