As I understand it, if the expansion was constant, farther away stuff would still be more red shifted. Stuff twice as far away appears to be moving twice as fas

As I understand it, if the expansion was constant, farther away stuff would still be more red shifted. Stuff twice as far away appears to be moving twice as fast. It helps me to imagine the expansion of a metal cookie sheet, where the two edges are moving apart faster relative to each other compared to the speed that they're moving away from the center. The surprising bit is that the far away stuff seems to be even more red shifted than that, so we're not just expanding, but the rate of expansion seems to be accelerating.