matter-to-matter couplings tend to be vastly stronger than matter-geometry coupling.I know that the supernova studies showed objects as more distant than expected, but if those objects are further away due to a stretching of spacetime then we should perceive an increase in object size. Matter is not independent of spacetime and surely must be affected by this stretching. Are those distant galaxies larger than expected? Has anyone tested for this?
So objects the size of galaxies hold themselves together at a stable size. The effect of geometry (Hubble-law distance growth) is not noticeable at that scale.
Personally I never talk about "stretching of spacetime". Or about "stretching of space". I don't think of space as a material. If you use the balloon analogy as a help, ignore the rubber. Pretend the rubber isn't there and that the picture is meant only to illustrate evolving geometry. The galaxies are not moving, they are only all getting farther apart. All existence concentrated on the infinitely thin sphere, no inside or outside, or rubber .
It takes some concentration to think in terms of an evolving geometry (rather than material being deformed stretched/compressed within a fixed geometry). But the concentration gets you closer to what GR is really saying.
"Dadurch verlieren Zeit und Raum den letzten Rest von physicalische Realität". In other words "it's not a material, don't think of it that way!"