When activating the evolution for a caught pokemon, it seems to amplify the CP. Thus it is most beneficial to evolve your pokemon with the highest CP, if you have multiple of the same kind. But what I am not sure about:

Does it make an efficiency difference, if you spend candies and dust to boost CP before evolving, to gain more from the amplification? Or is it more efficient to just evolve without spending, and then using the leftover candies afterwards, since they now give a bigger CP boost per candy? I only tested with a Rattata so far, which gained +8 CP per candy before evolving, and +15 CP afterwards. I collected no numbers on the amplification efficiency though, and now ran out of materials for further testing.

Or maybe it is a balanced calculation and makes no difference at all? I would love to have some insight on that.

Some data I collected this far: (GPC = CP gain per candy)

Weedle (GPC 6) evolved at 79 CP to a 84 CP Kakuna (GPC 6), evolved at 90 CP to a 297 CP Beedrill Note: The max-CP "half circle" in the profile stayed filled roughly at the same relative position throughout the evolutions.