Biography: 

Millennia ago, on a nondescript gas giant whirling about an unremarkable sun, a few carbon atoms formed a cloud of goo which was just a bit more interesting than its surroundings- It was alive. It was the first life on Balin, home to the Balinar, and as time marched on, it would grow, adapt, and evolve, eventually taking a form rather like a floating whale- the seeds of sentient life had come to the vast world of Balin. 

So had the Endless. 

In the midst of the great schism, with Concrete and Virtual engrossed in war, many nascent species were made into warrior-slaves, little more than cannon fodder. But some of the Endless wanted no part of the war, opting to use their technological prowess to bring beauty to the cosmos. And so, with careful injections of dust into Balin's atmosphere, the whale-like songs made by the Balinar were amplified, purified, and perfected in their very physiology. 

Though the Endless that created them departed, fleeing the war, the Balinar managed to perfect space flight in spite of their bulky form, reaching onward to the heavens. Soon, the whole of the galaxy will weep to hear the beauty of their voices.

Faction Affinity: 

Song of the Stars: The ruler of the empire may select one of the following empire-wide bonuses

Hymn of the Harvest: Boost to food production. Everyone knows plants grow better for a bit of singing, and there is no better singer anywhere than a Balinar.

Aria of Enlightenment: Boost to science production. This unimaginably complex piece seems to present a new face for analysis with each listening, stimulating scientific thought.

Intonation of Industry: Boost to industry production. Whistle while you work.

Epilogue of the Endless: Boost to Dust production. A musical tale recounting the elevation of the Balinar by the Endless, in which Dust played a key role, boosts production of the enigmatic substance.

Overture of Office: Boost to Influence production. When the Balinar sing of the glory of empire, you believe them.

Ode to Joy: Boost to approval. Written by the legendary Balinar Betho Venn, this song lifts even the gloomiest spirits.

Dirge for the Damned: Reduction of approval for all empires at war, or in cold war, with the Balinar. Increased war exhaustion generation for empires at war with the Balinar. When your opponent is already singing the hymn to your funeral, morale is going to suffer.

Join the Chorus: For each alliance on the Empire, the bonus from Song of the Stars is increased. Empires allied to the Balinar receive a portion of this bonus. (Half? One third?) From many voices, one song.

Faction Traits:

Big Boned: Reduction of population cap on most planet types (Non Gas Giants). While it would be disingenuous to call a species which is by necessity lighter than air "overweight", the Balinar do take up a considerable amount of space.

Bouyancy:  Bonus approval, FIDS, and Population cap on Gas Giants. Gas Giants can be colonized immediately. Some people just seem to float through life...

Siren Song: Propaganda is twice (Could be more, could be less) as effective for your empire. Hopefully this siren's song won't lead you to a watery grave.

Delicate: 50% reduction in effectiveness of ground troops (all stats) While the interior of a spaceship can be made to suit the bulbous and soft Balinar physiology, battlefields are less accommodating to a large, floating target than one might expect.

Population Bonus: Influence production per person per trade route. Like wandering bards of old, the influence of the Balinar is not to be had scheming in one's own home, but out among the masses. Trade routes spread your message, and your influence, across the galaxy.

Political Association: Pacifist (obviously). The guns of war drown out even the sweetest music, and the Balinar wish to be heard.

Rationale: I envision the Balinar as a race that works well diplomatically because war with them is just too costly. Putting aside the reasonable chance that they have allies backing them up, Dirge for the Damned exacerbates war exhaustion and makes fighting a drag on an opponents economy. The cost of war is even more significant when one counts the opportunity cost of not allying them (Losing out on a substantial bonus to FIDSI or approval). Moreover, their affinity for gas giants means they should be able to avoid stepping on other empires' toes fairly well- there should be significantly less competition for territory, at least until the late game when gas giants become colonizable for everyone else. This allows the Balinar to expand, gain enough of a foothold to be a worthwhile ally (aided by Join the Chorus) and establish themselves as a diplomatic powerhouse. Caution is required, however, as the value of an alliance is largely dependent on the size of said alliance- if one member leaves, they lose a lot and everyone else loses a little. If the Balinar are too aggressive or otherwise causing a nuisance, they may find themselves bereft of allies, and this not only minimizes the bonus they receive from Song of the Stars, but makes the bonus on alliance from Join the Chorus less tempting to a potential ally. 

In short, the Balinar will be an interesting and enjoyable faction to play, at least in my mind, because they are essentially striving to build a diplomatic house of cards- Dynamic, and capable of taking you quite high, but one mistake can cascade severely.

I was going to do a variation of whales in space but I saw you already beat me to it, so have my vote!