Sheer stability drops dramatically as the spread between the two numbers increases. This is the major reason why you cannot run 0w40's in most engines year round, or at least in areas that'll see extremely high ambient temps.
Basically, the oil viscosity index improvers responsible for making multiviscosity oils possible will "shear" and breakdown over time (how quick depends on drive cycle, ambient temps, engine design, load, etc.) and cause the oil to no longer be a 40 weight when hot. So what started out as a 0w40 may quickly become a 0w30 or even a lower. As that occurs, engine protection drops and reach a point where sludging, accelerated wear, and damage begin to take place.
This is a major reason why 10w40 was abandoned as a common weight many years ago. Being conventional oils, they caused a lot of problems because the additives weren't stable long term.
Modern synthetics and extended life additives allow some of these extreme weight spread oils to exist, but they still are susceptible to shearing, just less so.