female cat

Question
She has trouble digesting food?  Ends up coming back up.
Problem for some time.  She won't slow down eating.  
Her belly appears fat.  She is active and lovable regardless.

Answer
There are two main classifications of food that is brought back up regurgitation and vomiting.  If the food is pretty much in it's original undigested form this is called regurgitation.  If your cat tends to quickly inhale her food, especially dry food, water that she drinks afterwards can expand it and cause her to decide to regurgitate it back up.  This is a relatively common problem with cats.  You can try feeding her multiple small meals throughout the days so that the amount she can eat at one time is limited.

Her belly looking bloated could be possibly due to worms.  This as well as many other causes, including ones such as metabolic problems, viruses sand toxins can lead to vomiting.  The food will be more broken down and a more liquid nature to the vomited material.

I would recommend having your veterinarian give her a physical and do a fecal exam for parasites.  This will hopefully find or rule out the causes for her digestive difficulties.

Best of luck to you and your little darling.