Well in the GR sense, anyone or anything experiencing zero g-forces is in a rest frame i.e in 'free-fall'. We standing on Earth's surface are not, but move up a scale and Earth's center of mass is in free fall wrt the rest of the Solar system, and in turn our Solar system is in free fall wrt the rest of the galaxy, and in turn our galaxy is in free fall wrt our local galactic cluster, in turn in free fall wrt our super cluster. There are a few disconcerting exceptions but once you get to a few hundred million light-years in scale, things become essentially homogeneous and then out it's believed the (observable) universe can be treated as a uniformly dense continuum.
The cosmological principle then says an observer anywhere in the universe considers themselves to be at a center where all other large distance entities, as part of that uniformly dense continuum, are moving away from that observer in a spherically symmetric manner. And as you know, the further out from that center, the faster the apparent recession speed of distant objects becomes.Cosmological redshift.
What spoils it is the inhomogeneity at those smaller scales - being attracted to some higher density galaxy cluster/super-cluster leading to locally observed 'peculiar velocities' wrt the ultimate reference we have defining almost perfect homogeneity - the CMBR. It's because the fossil radiation of that CMBR has experienced negligible gravitation 'clumping' on it's journey over billions of years, and was initially so uniform at ~ 300,000 years post BB, it acts as that reference backdrop from which we can gauge our local deviation from perfectly symmetric Hubble flow centered about us.
Drop down to the expanding balloon analogy. Almost uniformly spaced dots on that balloon will see every other dot moving away with an apparent speed proportional to distance from it. But now allow that dot to move across the balloon surface, and moreover feel 2D gravity tugs from neighboring dots. If the distribution were entirely uniform, the reference dot will have no tendency to drift across the surface owing to symmetry of the collective tugs. Hence each is 'at rest' wrt the balloon surface. But with significant inhomogeneity of dot spacing, chances are our reference dot will feel a net tug in some direction and will thus start moving toward there. If we now throw in a diffuse, surface confined radiation, the dot motion is detectable via Doppler shift anisotropy - a so-called dipole anisotropy in particular.
Note the dot is still in 'free fall' thus 'at rest' in the sense of being 'weightless', but nevertheless has a motion wrt the balloon average dot distribution. In that sense it is 'not at rest'.
Hope I haven't confused you further!
