To be very precise, this is what happens:
As we are attracted towards the sun by the force of sun's gravity, we continuously experience a constantly increasing force, because of the inverse-square law.
And due to this, our momentum is continuously increasing.
This increase in the momentum causes a centripetal and a centrifugal force on the earth, which results into a helical orbit.
But due the inverse-square relationships, the horizontal component of the helix is nullified as soon as the earth achieves its stability, so it revolves around the sun, without crashing into it.
At this point, all of sun's gravitational pull equates mv^2/r, which in then accounts for all the centripetal force of the earth.
SO, THEREFORE, NO EXCESS FORCE PULLS THE EARTH FURTHER TOWARDS THE SUN, SINCE ALL OF THE FORCE IS EXPENDED IN MAKING IT REVOLVE.