Just one among the hundreds of baits thrown in the lake.
Weaknesses could be added for Eidolons, each one of which gives a set number of additional evolution points at the cost of its drawbacks.
For example (a quick and extreme example, just to show): Achilles' Heel - One of Eidolon's heels causes it to die instantly, if it takes damage equal or above 1/10 of the Eidolon's current HPs. The heel has AC equal to the AC of the Eidolon, plus 8 because of its size. This weakness grants 4 additional evolution points.
(This heel thing would call for rules about hitting specific locations, I know, but, as I said, it's just an example.)
These weaknesses could be of every kind: energy weakness (independent from presence or absence of immunity to the opposite energy type), lack of immunitary system (impossibility or huge penality to save against poisons and diseases), body parts that cause double damage when hit, blindness/deafness, slowness (capable of taking only one standard action or move action each round, like a Zombie), fragile bones (damage x 1.5 from bludgeoning sources), and so on.