1939 Wheat Penny Possibly Thin Planchette. Need Your Knowledge Please

I think you scale is fine, the wheatie should weigh around 3 gr (with wear), so we need to investigate why your coin is lighter than what it should be. We'll need better bigger photos, please, both sides. And if one edge is thinner, we'll need to see that too (prop it up somehow, without holding it).

You have come to the right place for answers.

to the CCF!

Here is an example of a pre strike lamination issue. Note the weakness of the design:



Here is a post strike lamination:



This will lighten the planchet/coin a bit.

These are cents that were dipped in acid to reduce thickness and diameter:



Weight will be reduced from the acid dip. But note the surface of the coin:

Appears to be an acid dipped coin. Things to look for:
Acid dipped coins can show these items.
1. Lighter weight of the coin.
2. Appearance of the coin with a rough texture. As if it were pressed with sandpaper, flat into the coin leaving incuse pock marks on the surface of the coin.
3. Rims will be affected first. The longer in the acid the more the rims are affected? Why? Acid attacks the surface of a coin. The longer it is left in acid, the more surface goes away. On the edge, there is a three side contact with acid. Top, Bottom and edge. This removes the rim/edges quicker because of the 3 side contact to the acid. Thus coins that have spent a long time in acid, can be very thin.
So look for these on your coin. I can already see #2 on your coin from the last image. So I feel that is what it is. But examine these for yourself. Because they are hands on teaching aids.