Perhaps the wrong questions are being asked. No it did not come out of the ground at least not in the last 50 years. No assumption of weight leaving the mint is being made. Weight is an observation of what this coin with oxidation but otherwise good shape is. Weight is an observation of what 1898 1C are supposed to leave the mint at. I tell my graduate students we have to ask better questions. I am new to collecting but not to Science. What would I pay is a fair question if I were presenting this as a question of monetary value.
Perhaps comparing the coin to another 1898 would be helpful. The new picture is a much more circulated example. Its weigh is 2.97.