8-10 pounds is an average weight for cats in general. The test for too thin is the skin being thin over the ribs and being able to feel the ribs with very little tissue between your fingers and the bone.
Some cats beg for canned food. They may not be hungry, but like the wet food.
Cats vomit easily. In a species that naturally eats other small animals, vomiting is a good way to get rid of indigestible parts such as hair, skin and bones. How often does she vomit? How long has she been doing this? Does she usually vomit food or hairballs or something else?
Hairballs are common in spring and fall during shedding season. Adding psyllium or petroleum jelly (Vaseline) to the food can reduce the vomiting caused by hair in the intestines.
If she is vomiting often (daily or thereabouts) the most probable diagnosis is inflammatory bowel disease. The exact cause of this is not known and may be different things. Food allergy may be one part of this syndrome. Changing food can help, but the change has to be to a diet based on one protein and one carbohydrate. Usually we try to pick foods they have not previously been fed. Examples are duck and potato, lamb and rice, chicken and rice, fish and sweet potato, etc. These are available from your vet and also from some commercial companies. You can find them by Googling "cat food duck potato." The food is expensive from vets or the internet.
Diet is rarely a cure, but helps. Prednisone may be added to suppress the immune reaction or allergic component and inflammation. Other drugs may be needed.
Diagnosis is based on a history, physical exam and diagnostic tests (blood work, urinalysis, fecal analysis, intestinal biopsies....). A accurate diagnosis allows the treatment to be tailored to the actual problem.
Let me know if you have follow up questions.