How to help my rival against awakened empire

I played a game where something similar happened, though the other empires were more neutral to me. The only way I found to stop the Awakened Empire conquering all the other guys and becoming unstoppable was to attack them myself. I basically waited till there was a war and then jumped in and took the Awakened Empire's nearest planets while they were chasing the other Empire's fleets until I had enough warscore to win, I claimed their core worlds first to hit them hardest and gain the biggest benefit.

Unfortunately I didn't finish the game as I reached a kind of stalemate where I couldn't easily challenge the AE any more and got bored.

So I think the best way you can help is to capitalise on the situation yourself and weaken the AE if you are in a position to do so. No matter how much you give to the other empires they will never really be a match for the AE.

I'd advise against sending the rival resources, for two reason. First, they're unlikely to help much. Your rival may be able to build a few more ships with them, but it's unlikely they'll be able to prolong the war by much.

Second, you need those resources. You said yourself that you need to prepare- spend them on yourself (or your allies) to build more ships and shipyards, or as a reserve to replace losses.

Letting the AE win is not necessary a bad thing.

The awakened empire starts generating decadence - a big penalty to produced resources and fleet capacity - and speed it is generated is proportional to the size of the empire.

Decadence is effectively a meter, going from 0 to 100, that starts filling up for Awakened Empires once a certain amount of time has passed since awakening. The larger they are (both in terms of owned planets and subjugated empires), the faster it builds up. Decadence reduces Awakened Empire resource income and fleet power, and also increases the rebelliousness of their subjects, and has very large penalties at high levels of Decadence. What this means it that while an Awakened Empire might start very strong, and grow even stronger as they expand, that very expansion will eventually turn into decline, until they're weakened to the point where the rest of the galaxy can rebel and overthrow them - if you end up their subject, you just have to be patient, build up your forces, and wait for the right moment to take back your freedom

Source

So if the AE will attack and conquer your rivals it will in fact weaken itself and your rival and then you can conquer them both.