I don't think that there is an etymological commonality.
Upekkha is usually translated as ' equanimity ' or ( very badly ) as ' indifference '
The roots of the Pali are " upa " ..towards, bringing to the fore, and "ikh " to see...
So something that is seen in balance or in the context of something wider..
By contrast Apekkha is usually translated as desire...a longing for.
A translation could be ' that which is seen in isolation from context..'
For example we look into a shop window and see a tray of buns and they dominate our attention..
That is Apekkha..
We look in a shop window we see a range of goods to which we are neither averse nor are we overwhelmed by their attractiveness...that is Upekkha.