Before a pullet or hen even starts to lay she builds up excess fat. A lot of that is in a fat pad in the pelvic area but you can have more fat in various places. This excess fat is what a broody hen mostly lives off of so she can spend her time on the nest taking care of the eggs instead of having to be out looking for food. To me it is normal for a pullet or hen to have a lot more fat than a male. My hens pretty much all go broody so they may have more fat than some others. But I'd consider it abnormal if a pullet or hen did not have a fairly large amount of fat compared to the boys.
I regularly butcher pullets, hens, cockerels, and roosters. The boys have very little fat, the girls usually have a lot. If you are wanting to make schmaltz (rendered chicken fat used in some cooking) you need to butcher a hen to get a reasonable amount. The boys won't have much fat, the girls should have quite a bit comparatively.
Fatty liver syndrome in chickens is real. From what I read it is generally associated with lack or activity (exercise) and a high energy diet. Fat builds up in the liver which makes it subject to hemorrhaging. There are typically no warning signs until the chicken dies.
I do not know how to distinguish between normal fat build-up in the body cavity of a pullet or hen and fatty liver syndrome. Because of all of the fat I see in the body cavities of pullets and hens I butcher I would not worry with yours. Mine have a lot of fat and they are not dropping dead from fatty liver syndrome. Did you notice if the liver was a normal color or if it was pretty pale?
