In some cases... the older the engine, the more worn the piston rings / cylinders, the more oil your likely to burn. As a thicker oil is harder to force past the rings, in theory, the less you'll burn... some say a 5W40 oil is too thin anyway - my local specialist (S4U) uses 10W50 oil.
Sometimes, mineral oils are recommended for higher mileage engines too... something about helping to soften the piston rings and helping them fit more tightly in the cylinder.