You're confusing work (pushing the two masses) with acceleration. When objects are accelerating due to gravity, the mass of the object doesn't matter. Galileo demonstrated this by dropping a cannon ball and a bullet from a height, and they hit the ground at the same time. So no, gravity doesn't 'push' or 'pull' either upwards or downwards - is an attractive force between two masses.
Boru
Boru
‘But it does me no injury for my neighbour to say there are twenty gods or no gods. It neither picks my pocket nor breaks my leg.’ - Thomas Jefferson