Can an attacker change an old block without changing the checksum? Since multiple values can result in the same hash, couldn’t an attacker try to find a way of increasing his balance in a way that the checksum of the changed block remains the same (so that any proofs-of-work are still valid) and then propagate the change into the network without peers noticing it?
Sure, he can try. But the algorithms Bitcoin uses were specifically chosen to make this attack completely impractical. It would be trillions of times easier to just buy the Bitcoins.