Hello. I'm sorry to hear about your cat.
One episode of vomiting with some blood doesn't bother me. The weight loss and decreased appetite have me worried. This could be one of many things- an obstruction, cancer, IBD (inflammatory bowel disease), an infection, ulcers, ect.
I would start with bloodwork and x-rays to look for metabolic disease or an obstruction. We may also see a large mass on x-rays. If everything is normal, I may consider an exploratory surgery. This is to look for masses that do not show up on x-ray and to biopsy the stomach, small intestines and lymph nodes. The biopsies differentiate cancer from IBD.
If you don't want to go forward with an exploratory surgery, many people will just try steroids as it helps with cancer and IBD. We don't know the long term prognosis at that time, but it can help with the signs and get these guys feeling better for a time.
I hope this helps, let me know if you have any other questions.