Pardon me if I am being impatient. but I noticed there are several fattened up sprites of regular enemies in the game. How do enemy battle sprites get fattened up? 

SPOILERS: There are two ways to fatten enemies currently. The first is by recruiting the secret character, Elmira. If you bring Abby back to the Inn in Crabshoot Bay and talk to the blonde singer, it'll start a questline that ends with her joining the party. She has the power to fatten enemies using her Adipomancy skill!
The second way is through the Calorie Bomb item, which is very rare and only really found later in the game. There's a sidequest involving Ashley later on which gives you a few Calorie Bombs to use.