Ascites: This is the most likely diagnosis given the patient's history of metastatic liver cancer. Ascites, which is the accumulation of fluid in the peritoneal cavity, is a common complication of liver disease, including liver cancer. The weight gain in the abdominal area without a change in diet strongly suggests ascites.

Abdominal tumor growth: The patient's metastatic liver cancer could be progressing, leading to an increase in tumor size, which would cause weight gain in the abdominal area.
Liver dysfunction: As liver cancer progresses, liver function can decline, leading to fluid retention and weight gain.
Hepatic congestion: If the liver cancer is causing hepatic vein obstruction, it could lead to hepatic congestion, resulting in fluid accumulation and weight gain in the abdominal area.

Bowel obstruction: Although less likely, a bowel obstruction could cause abdominal distension and weight gain. This is a potentially life-threatening condition that requires prompt diagnosis and treatment.
Intra-abdominal hemorrhage: Bleeding into the abdominal cavity, possibly due to the cancer or other causes, is a medical emergency that could present with abdominal distension and weight gain.
Spontaneous bacterial peritonitis (SBP): This is an infection of the ascitic fluid and can be a complication of ascites. It is a serious condition that requires prompt antibiotic treatment.

Ovarian cancer: Although rare, ovarian cancer can cause ascites and abdominal weight gain. This would be an unusual presentation for a patient with known metastatic liver cancer, but it should be considered if other diagnoses are ruled out.
Lymphoma: Abdominal lymphoma could cause weight gain and abdominal distension, but this would be an unusual diagnosis in a patient with known metastatic liver cancer.
Tuberculous peritonitis: This is a rare condition caused by tuberculosis infection of the peritoneum, which could cause ascites and abdominal weight gain. It is more common in immunocompromised patients or those from endemic areas.