By what mechanism does coeliac disease cause excess fat in the feces?
Coeliac disease is an immune disorder resulting from a reaction to ingested gluten (a protein found in wheat, barley and rye). It is associated with inflammation of the small intestine resulting in a generalised reduction in the capacity for digestion and absorption. According to this paper:


  Celiac disease is associated with pancreatico-biliary disease. Postulated mechanisms include reduced gallbladder emptying due to impaired cholecystokinin release and pancreatitis due to malnutrition.


Cholecystokinin is a peptide hormone that is produced by specialised cells in the small intestine and which stimulates the production and release of pancreatic enzymes and bile. Digestion of fat is critically dependent upon the emulsifying properties of bile salts in bile, together with pancreatic lipase. Any breakdown in this stimulatory pathway would result in reduced capacity for digestion of dietary fat.

Failure to digest fat results in fatty stools (steatorrhoea) which is one of the classic symptoms of the disorder.