I've read all of the viscosity-wear studies I could get my hands on. The general study design is to operate an engine at high load with high oil temperatures (usually 130°C in the sump), with several different grades of oil, most of them thinner than what was originally intended for the engine.
The common theme in these studies is that the piston rings are the most sensitive part of the engine to increased wear from thin oil grades. This is because the oil film at the rings can approach the temperature of the rings and upper cylinder liner, which get very hot at high engine loads. Shear rates are also high at the piston rings.
Ring wear may increase to 2 to 4 times the normal wear rate when the oil is multiple grades thinner than the intended grade. This only occurs at high engine temperature and high load, so for your typical commuter car, these events should be rare, and should have a negligible impact on the lifespan of the rings.
Most other parts of an engine are completely insensitive to viscosity in these tests. Compared to the piston rings, the oil films at most other components operate much cooler, so the viscosity won't get anywhere near thin enough to start causing increased wear. These are parts like timing chains and gears, oil pumps, and low-friction valvetrains. Basically, an automaker will select an oil grade that provides adequate piston ring protection, and this grade will always be thicker than necessary for most other engine components.
There are some exceptions, like flat tappet valvetrains that have high friction and extreme shear rates, which can get the oil film about as thin as it is at the piston rings. These valvetrains can have increased wear with thinner oil grades, but the increase in wear is pretty modest.
Rod bearings aren't very sensitive to viscosity until the oil gets so thin that oil pressure drops below a critical level, at which point catastrophic wear will occur. This is due to centrifugal forces interrupting the supply of oil below a certain minimum pressure, which increases with rpm. Main bearings and cam bearings don't experience this type of catastrophic wear.
So while the rod bearings won't usually see increased wear as soon as the rings do, the consequences of low viscosity can be far worse. This shouldn't be much of a concern for most engines unless there are other problems that are also causing reduced oil pressure (extreme oil temperature, foaming, aeration, clogged oil filter, etc.). A thicker grade will provide a larger factor of safety for this type of bearing damage, but won't have much effect on normal wear. One study shows a reduction in normal bearing wear with thinner oil grades.
