Mom has a swollen abdomen, with very little fat elsewhere, what is going on?

Fluid or ascites. Your mom needs doctor evaluation. If she is otherwise okay, abdomen getting more swollen over six months, it could be fluid expanding her abdomen. There are several other possible causes; mass, metabolic, enlarging liver and spleen. Fluid could be from cancer and/or liver dysfunction. An ultrasound will make the diagnosis. Fluid can be tapped, evaluated and treatments started. Don't delay.
See a doctor ASAP. If the abdomen has become swollen over a short period of time, this can be a sign of bad things such as: ovarian cancer, liver problems, benign ovarian mass, and many others. Do not wait, go see a doctor right away. It might also be simpler things like a hernia or weakening of the anterior abdominal wall or just ageing changes but do not wait.