If you think about it, at some point, almost all of the AS have been under the cook, if only during punishments. This has to lend an interesting dynamic to the kitchen. The WT Cook is in an interesting position. Not to mention that we all know how servants gossip, and she's a leading servant in the White Tower. Even if she is no directly involved in the tower politics, I am positive she is fully aware of all of them, and probably knows more about what goes on in the Tower than many of the Aes Sedai themselves.

With knowledge, comes opinion. It is likely she simply decided she would prefer to support Siuan and Leanne (and their "chosen" successor, Egwene) than support the tower usurpers.

As for "heavy but light on her feet", that seems to describe most fat characters in WoT

I could see her possibly being a failed initiate, but I don't think there's anything more special to her than that.