How does evolving relate to CP?

What I mean is how does the game increase the CP of an evolving pokemon? For instance I have a pidgey (278CP) when I evolved it became a pidgeotto (489CP), but when I leveled up my weedle (140CP) it became kakuna (150CP).

With some pokemon it seems to be doubled, others tripled, and some not at all

It's based on the level (the pokemon's progress on the semicircle) and the species. Level doesn't actually change on evolving, so this question is entirely about the species.

Kakuna and Metapod are renowned for being useless stages between weedle/caterpie and beedrill/butterfree. Consequently, a kakuna of any level is going to be fairly weak.