I received this note on the engraved 1840-O half dollar previously mentioned in the E-Gobrecht and E-Sylum. Paul's explanation is the best I've heard and the most logical I've heard by far by far.

I propose a reason for the engraved weight on the 1840 dollar coin. When a scale must be calibrated or proven to be accurate, a standardized weight of known certain value must be used to compare with the weight that the scale indicates for it. Nowadays, you can purchase standards at the National Institute of Standards and Technology, known for many years as the National Bureau of Standards. A century or more ago, someone probably wanted to calibrate their scale, and so weighed your coin on a scale that was trusted and known to be accurate, and then used that known weight to test their own scale which was perhaps uncertain. A coin is ideal, since it is corrosion resistant (won't change in weight) and rather wear resistant too.