They're not called that because they're fat. Because they're not fat. Sure, they seem to be blistering out of their skin but that's glandular. Too many chronotons. (If you thought we were going to go an entire KYL about dragons who want to alter the fabric of time and space and not once mention Futurama, well, you were wrong, Mister I'm my own grandpa. Now let's steal the dish and go home.)
The Infinite Dragonflight are a conundrum. In many ways, they're the opposite number of the Bronze Dragonflight, with an agenda wholly opposed to that of the stewards of time. Where the Bronze seem to shepherd time along its normal flow and prevent strange incursions, the Infinites are all about strange incursions. Strange incursions that seem to be aiming at nothing more and nothing less than the total destruction of the established history of Azeroth proper and the creation of a wholly new order.
- We don't know when, exactly, they exist. Since they travel through time to alter history and we have no idea where/when their home base is, they could be from the distant past (one of those 'other dragonflights' that existed before the Titans made the five aspects from Galakrond) or from the future, or an alternate timeline or timelines (perhaps created when a dragon, an elf and an orc went back in time and totally messed with the lore...er, I mean changed history).
- We don't know who they ultimately answer to. We know that when Epoch Hunter dies after you prevent him from killing Thrall in the past as he escapes from Durnholde, the drake says "the master will not be pleased" but who the master is, we don't know. There's lots of theories but not many facts at present. Are they related to the time storm that trapped Nozdormu in the novel series related to the War of the Ancients? Or do they have a more straightforward and sinister relationship to the Aspect of Time?
- We don't know what their ultimate goals are. We know that they travel through time to key points in history (the escape from Durnholde Keep, the opening of the Dark Portal, the culling of the citizens of Stratholme) and that they were attempting to alter the events at Mount Hyjal in some fashion (forcing Soridormi of the Bronze Flight to breach a barrier and send agents to ensure time's correct flow) and we know that they're locked in what appears to be a kind of time-shifting combat at the Bronze Dragonshrine, but what we don't know is why. Sometimes they make comments that seem to indicate that they believe that they're after some kind of greater good, but at others they just seem blatantly malicious.
- We don't know how they come to be. We know that there is at least one case of a member of this flight (the Infinite Corruptor) attacking a member of the Bronze in a way that seems to indicate at least some of the Infinites are or were members of the Bronze Dragonflight who were changed either willingly or against their will. How this process functions (it seems to take at least 25 uninterrupted minutes to accomplish it) and what it really even does (does it kill the original and make an Infinite in its place, warp it in a manner similar to fel corruption, compel obedience, brainwash?) is as yet unknown, as is whether or not this is the only means to making an Infinite.
Each incursion by the Infinite Dragonflight seems aimed at either preventing the existence of the Horde or of the Burning Legion's most recent invasion of Azeroth. If Medivh does not open the Dark Portal, there is no First War, as the orcish tools of Kil'jaeden would have died on their diseased husk of a planet without the portals to escape through. No Alliance Expedition, no Ner'zhul recklessly opening portals, no Netherwing, no destruction of Draenor, no escape of the Exodar, no Draenei on Azeroth, no Lich King, and nothing to point Kil'Jaeden to the world his 'master' (it's fairly clear that neither Archimonde nor Kil'jaeden feel a terribly strong loyalty to Sargeras) lay trapped on.
In addition to attempting to stop this event, they also attack other key points in time that would have accomplished some of these aims. By trying to prevent Thrall from rising to leadership of the Horde, they would remove the New Horde from the events of history - no death of Cenarius, no Hellscream's redemption against Mannoroth, no Horde presence on Mount Hyjal at all. Meanwhile, by killing Arthas (or at least preventing him from finding the tainted grain in Stratholme and launching his purge of the city) they would prevent the rise of one of the Legion's most effective servants, as it was wholly via the actions of this death knight that the lick Kel'Thuzad returned from death to summon Archimonde to Azeroth. But we can clearly see that their primary goal was merely to prevent the culling of the city. Why is this? What would they have to gain from the city falling to the plague before Arthas could kill the inhabitants? They went with their backup plan of outright killing Arthas before he could reach Mal'Ganis only after their initial plan to delay Arthas' awareness of the tainted grain was foiled by Chromie of the Bronze Dragonflight and her allies.
(Editor's note: I made a mistake here and said Chromie was in the Infinite Dragonflight, and not the Bronze. Several people caught the error in the comments..)
So look at the basic events as they would have unfolded: if the Infinites had successfully either slain or kept Thrall enslaves, then the soldiers of Lordaeron who were out looking for him and his Horde post-Durnholde would have been free for other duties. Northern Lordaeron would have had its usual defenses, meaning that roaming paladins like Uther and Arthas wouldn't have been forced to deal with situations like the orcs attacking Strahnbad. Furthermore, with the forces of Lordaeron not divided and Arthas and Uther working together to contain the plagued inhabitants of Stratholme (who would have had time to fully turn if Arthas had not discovered the tainted grain there as quickly as he did in established history) then there would have been no reason not to burn the city and no one would have objected, and Arthas would have had the full assistance of Uther and Jaina against Mal'Ganis there. We know, too, that Chromie sensed temporal incursions at Andorhal years later, incursions she blamed on the Scourge at that time. Since the Scourge has shown no further ability to travel in time, and since we clearly have sizable evidence of Infinite interest in the fall of Lordaeron, we can dismiss the Scourge and focus on the Infinites.
In every case where they take an active interest (despite their being evidence of their interference with the battle of Mount Hyjal, once you travel to that battle through time you see not a sight of them) they're attempting to prevent either the Legion or its major tools of conquest, the Old Horde/Scourge, from reaching Azeroth. Failing that, they seek to minimize their effectiveness. How will this 'shatter this clockwork universe' exactly?
We know the Old Gods can manipulate time, and that Nozdormu can check their influence. We know that we've seen at least one example of a temporal incursion into the past that was successful, when a Dragon, a wizard and an orc went back in time and, while preserving the rough outlines of the War of the Ancients utterly changed their particulars (an orc on Azeroth before the Sundering who injured Sargeras himself?) and it was, supposedly, Nozdormu who caused it by sending them back in the first place. We are led to consider the following possible scenario for what is happening. What if the Old Gods tricked Nozdormu into changing history?
Imagine that the 'time storm' that ensnared Nozdormu and forced him to send back three agents to prevent tampering with the past (which they do in broad strokes... the Legion is defeated, the Sundering happens... but in a great many particulars the events of the War of the Ancients with Krasus, Rhonin and Broxigar involved barely resemble those we hear about in the WCIII manual) was created by Nozdormu sending them back in the first place. A new timeline is created that mostly resembles the old, and the World of Warcraft that we as players would recognize is that timeline. As a result, 'our' timeline's Nozdormu doesn't have to send anyone back in time since it was the Nozdormu of that previous timeline that sent them back. That Nozdormu, Aspect of Time charged with guarding and securing the flow of history, has instead deliberately and willfully sent agents back in time and altered history.
What happens when the Aspect of Time changes time's flow? What happens to a Dragonflight dedicated to preserving history that perverts it? Are they corrupted? We can postulate that it is the Nozdormu of the original timeline who seeks to prevent himself from having ever sent back a human, dragon and orc and thus changing history by taking various actions aimed at preventing those people from either existing or being in a place to assist him. No First War because the orcs never come to Azeroth? No Broxigar to send back to become the only mortal to ever wound Sargeras. No need for Rhonin to free Alexstrasza from Grim Batol, no need for the Aspects to regain their power from the Demon Soul, no need for Krasus to reveal himself to the mage at all. If you can stop any of the wars... First, Second or Third... you stand a chance of preventing Broxigar from having the drive necessary to make the attack on Sargeras at all, in fact.
Imagine the Infinite Dragonflight as a perversion of the Bronzes and their goal, created by an Aspect's mistake. (We know they can make them, now, as we've seen with Malygos.) However, since we're dealing with time and time travel, it's possible that Nozdormu doesn't even know it happened, since it didn't actually happen to the 'him' we would know. He and his Bronzes may in fact be under attack by what is, essentially, the original timeline trying desperately to prevent itself from being overwritten with the only means at its disposal, attempting to shatter the clockwork universe rather than being ground up by its gears.
In the end, however, what we know about the Infinites is their actions. They attack time, they corrupt Bronze dragons, and they cloak a ruthless willingness to destroy the past with honeyed words of a better future. All else is speculation.