I think a clue was the way red-shift correlates with distance. Either we're really at the center of the universe and the whole thing is moving away from us or the whole blob is expanding and diffusing. The former position looks attractive to some people but there's a lack of corroborating evidence that our corner of the universe is that special.
Similarily, general relativity accounts for gravity due to space curving, but curving relative to what, meta-space?
You can see the curvature of space when dense foreground objects lens galaxies behind them, or the sun subtly shifts the apparent position (as seen from earth) of a star behind it. Thus, you can say "curving relative to less-curved space." At any rate, this action of mass on space is well documented now.
You can't, for the same reason that you can't tell the difference between acceleration due to gravity when you're sitting in a chair at home, and acceleration from a rocket, when you're sitting in the pilot's seat. This is known as the "equivalence principle", and there are different formulations of it. It's a big topic.
Similarily, general relativity accounts for gravity due to space curving, but curving relative to what, meta-space?
Have you ever played the game "Asteroids"? If you move your ship past the left-hand edge of the screen, it appears on the right-hand edge; if you move your ship past the top of the screen, it appears on the bottom. The space in which the ship moves, therefore, is shaped like the surface of a doughnut. (Take a rubber sheet and connect the left-hand side to the right-hand side, and you get a tube. Bend the tube around so that the top edge mates with the bottom edge, and you have a doughnut.)
Now, when you're playing the game, where is the doughnut? In what space does the doughnut exist?