The words diploma and diplomacy seem like they must share a root, but they have widely differing meanings. Where is the common ground?
At first I thought of the French nom de plume, literally pen-name, where the plume means pen and is probably derived from the same place as the English plume as in feather (think quill pens).
It looks like this is dead wrong, though: diploma and diplomacy come from the Greek diploma meaning, originally, "a paper folded double," from diplo-, meaning double. We still use the prefix diplo- to mean double in English. For example, diploid cell, a cell where there are two versions of each chromosome (the chromosomes are doubled).
However, it looks like the words duplicate and double do not come from the Greek diplo-, but rather from Latin duplus, du- (two) + plus (-fold), meaning, literally, twofold (but not fold as in the sense of "a paper folded double," rather in the sense of "a twofold increase in profits").
So. Not what I was hoping for, but still interesting.