Well for starters, the sun's gravity can't change unless it gains mass or loses mass. If it gains or loses enough mass to cause a noticeable change in gravity (say, .1%) there will be other powerful events associated with that. So whatever causes even a small change in the sun's gravity would probably be a traumatic event to the solar system.
If it's magnetic effects change, which I suppose is possible, it could do a number of things. Earth is a finely tuned instrument, and any notable changes to the sun's magnetic field have the possibility of devastating the life on earth.
Purely technically speaking, if the sun loses or gains gravity, it will have a corresponding effect on the distance earth orbits. If its gravity lessens, earth will go into a further orbit with a longer year. All other factors aside, it could easily throw the Earth into an ice age, devastating all but the simplest of life. A slight increase in gravity would likely have an equally devastating effect.