The earth is being pushed, not pulled. That was quote a bit of typing you could have saved yourself with a 30 second perusal of the FAQ.
Long time ago I saw a hypothesis that says it, but I can't find it for some time now.
It was going something like this:
"There is an universal isotropic 'pressure by neutrinos' (or by the dark matter maybe?)
which has been shielded by any mass, depending on its density and size,
reducing the pressure in the direction from the said mass,
while from the other directions the pressure remains unobstructed, keeping the original intensity.
That's why masses get pushed toward each other."
Ofcourse in that hypothesis there is lot of things that won't fit in the observed behavior, as described by the General Realtivity.
(Time dilatation, space-time distortion, Doppler on light beams, ...)
I think I see why I can't find it anywhere any more.