According to this article, oil viscosity does effect fuel mileage.
This particular test was done using a diesel engine in a controlled environment by Chevron engineers.
They used 15W-30 and data collected against the use of 15W-40 showed a %0.8 percentage difference between the two with the 15W-30 winning out on the better mileage.
The delta was attributed to the work of the oil pump on thicker or thinner oils. The piston moving within the cylinders would, more than likely, be unaffected by a slightly thicker or thinner oil as the piston is not pumping the oil, it's merely using it as a lubricant. The friction co-efficient between the two is nominal.
It is possible that you may have a slight decrease in engine noise, especially with straight cut gears within the motor that tend to be louder. This would typically only apply to very high performance cars though.