The most likely diagnosis is celiac disease. This patient has the combination of loose stools, unintentional weight loss, elevated liver chemistry test results, and iron deficiency anemia without an obvious source of blood loss. Minor elevations of serum aminotransferase levels are found in up to 50% of patients with celiac disease and may be the only presenting feature in approximately 9% of patients. Serum aspartate aminotransferase (AST) is usually less than 80 U/L, and alanine aminotransferase (ALT) is usually less than 130 U/L.