Complete layman, so take this with a grain of salt, but isn't the relativistic view of gravity that it bends space-time? So when you're in free fall you appear to be accelerating with respect to the ground, but you're actually in an innersial reference frame, while the ground is accelerating upwards through ever contacting space.

If gravity contacts space, then of course it will counteract the expansion of space.

You seem to be thinking relativistically about the expansion of the universe, but Newtonianly about gravity.