My sister had pleural empyema in a collapsed lung. The doctor avoided thoracotomy as being underweight, she might not cope with the anesthesia. What should I do?

Decision. Your doctor considered many factors when he did not take your sister for surgery. Talk to him to get explanation.
Empyema. Can be treated with percutaneous catheter drainage and tpa (alteplase) therapy to the pleural space along with the appropriate antibiotics. If this fails video assisted thoracotomy or vats may be performed. True thoracotomy only needed if these procedures fail. I use cat scan guidance to do the drainage and it works well.
Nutrition consult. Most cases of empyema may be managed without thoracotomy, by the use of less invasive procedures. Your sister's low weight is an issue that may impact her overall recovery. I would suggest a nutrition consultation as well to help her recovery. Determining the underlying cause of her infection is part of the management.
Talk with MD. The size of a patient is not necessarily a contraindication to anesthesia. After all we do anesthesia on children weighing only one or two pounds when needed. Your sister should discuss her case with the surgeon and anesthesiologist to see if there are any other complicating factors that might rule out surgery. Hope that this helps.
Agree. As dr. Korona answered, true thoracotomy is often an unnecessary (and poetntially more dangerous) approach. Modern thoracic surgical management of empyema uses, when appropriate, minimally invasive techniques. These include percutaneous drainage, medication instillation (i.e. Tpa), etc... Most important factor of treatment is early recognition and drainage.