I would not be so quick to say that the for sure the half dime is a counterfeit. I have seen this happen on legit silver coins, and I have a half dime that is somewhat similar in appearance and I believe the damage happens because of the coin being so small and thin to begin with, that sometimes when ground conditions are rough, and evidently they were by evidenced of the bad condition of the other coins found, that the 10% copper that is in the half dime may have reacted with the soil and started to "leach out" (for lack of a better word).
I weighed my 1842 that has similar characteristics and it is within the tolerances of a legit half dime. I do suggest checking the rim, I believe it has been said before on this forum that counterfeiters had a hard time getting the reeded edge on their counterfeits, mine has a nice reeded edge.
Also, as stated earlier, the counterfeits shown before, have flaws in uneven dates, lettering, different wreath designs, etc, not sure I see any of that on the 1839. Also the 1861 example in the other post is stated by PCGS to be the first year known where that type was "struck", before that they must have been cast copies I reckon.
Don