(Spoilers Main) My New Unhinged Theory: Thin Illyrio

Magister Illyrio isn't actually fat. Or at least not as fat as he looks. The biggest piece of evidence is that he's able to hop on a boat and cross the Narrow Sea and then sneak into the Red Keep's dungeon through some secret passage. He claims he's too fat to travel, but obviously that's just him making himself seem fatter and more helpless than he really is.

This is the same tactic that Wyman Manderly uses to get everyone to underestimate him and not suspect his hour-long privy sessions. Now I do think Manderly is just as fat as he thinks he is, but he knows how to play it up. With Illyrio I think there might be something else going on.

Pentos and King's Landing aren't that far away from each other, but still someone as obese as Illyrio should have trouble with basic mobility, let alone sneaking through a city unseen and then climbing up a cliff face and skulking around a dungeon like he must've. He's extremely noticeable the same way The Mountain is, although the fact that he's in league with Varys explains why no reports of him made it to anyone on the Small Council. It'd still be a lot easier for him to move stealthily from one major city to another without anyone knowing if he had a glamour.

He wears a lot of rings with different gemstones on them, and it seems like they were made for someone with much thinner fingers. It's not inconceivable that he could be working a glamour to make him appear much fatter than he really is. If dudes like Stannis Baratheon and Beric Dondarion can find powerful sorcerors I don't think it's inconceivable that Illyrio could find a red priest or some kind of mage to work for him. And we know for a fact he used to be extremely lithe and agile when he was younger.

It's noted that he moves surprisingly gracefully despite being so fat, so that's something. He also says at one point that he fucked one of his servants "vigorously" which if he's really so obese that he has to be carried around in a litter might be difficult.