The answer is somewhat complex, but think of gravity as light. The gravitational influence radiates, and as the distance from the source increases, the amount of influence decreases. Just as the apparent light from a lightsource fades as you get further from the source. Interesting, gravitational influence is thought to travel at the speed of light. Which means that in earth were to suddenly double in mass, and let out a burst of light at the same moment, the gravitational influence at any given point would be doubled only as the light pulse passed it. So the gravitational influence of the Earth is felt at the limits of the visible universe. As for the amount it is theoretically felt at all points within that sphere in, as you put it, insignificant amounts.
Notes:
This assumes the Earth has been a stagnant feature in the universe, or that we count the pre-earth material thus adding a HUGE degree of complexity, and arbitrary terms.
Light can be blocked by opaque matter, but gravitational influence is not (as we currently understand it) blocked by anything.
The influence is "insignificant" beyond the hill sphere of Earth, though some noticeable effects throughout our solar system, which leads us to the somewhat troublesome and hard to precisely define "sphere of influence".
I'm just a nerd, and this is based off my current understanding which is likely wrong somewhere.