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From looking at the surface of the coin it appears to be corroded - or perhaps it was treated with acid. But these type of manufactured errors generally only occur with cents dated '82 or later.
The planchet is definitely thicker and I wondered about it perhaps being struck on a nickel planchet. But the weight and the diameter rule that out. I must assume that even though you say by using the balance test the coin is usually heavier than a normal cent that it is only slightly heavier because it does balance out sometimes.
I'm not going to go out on limb here and say it may be an aluminum cent. But it might be even though I doubt it. I don't recall ever hearing that the planchets for the experimental aluminum cents were thicker but who knows.
Short of doing a specific gravity test I don't know how to indentify the metal. But you could try taking the coin to a metalurgist and get his opinion. You could also take or send the coin to an error specialist and see what they say. But it does appear that it may be an off-metal coin. Whether that would be the result of being struck on a foriegn planchet or an experimental planchet could only determined by testing.
I would be curious to hear the results if you do have it tested though.
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