How does the Sun's mass affect its evolution?
It determines its life span and the stages therin.
Larger stars are more unstable and therefore have shorter lifespans that take less time. While smaller stars are just the opposite. Our sun is about average and while have an average lifespan therefore.
The mass of a star also helps in the results of the star "dying." Heavier stars will explode or will collapse on themselves in a way that results in a supernova, black hole or a planetary nebula. Lighter stars may simply explode, may fizzle out or may lose their outer shell, or atmosphere.