As I understand it, it becomes ever more difficult to maintain a coherent quantum state among larger and larger collections of particles (this is why making large quantum computers is difficult), so for most practical purposes large aggregates of particles behave like a single "world". But there is no sharp dividing line, and the same math applies at all scales.
Unfortunately, this is where the imperfect mapping to which I referred above — between the math and our intuition — becomes misleading, and why I don't like the term "world" to begin with.
But still, the problem I was questioning was different: you are saying "there is one of us in each world". In fact, that is not what QM predicts: in QM, there is only one of us in the entire system described by the wave function, with different amplitudes in different states. A system with 1 electron with some amplitude < 1 in state A and some amplitude < 1 in state B is not the same as a system with 2 electrons, one with amplitude 1 in state A and another with amplitude 1 in state B.
So, if we took a detector that could measure state A or state B, we should expect that it detects state A with some amplitude and, simultaneously, state B with some other amplitude. Instead, MWI postulates that there are 2 detectors, one which measures state A with amplitude 1, and the other state B with amplitude 1 (in fact, it postulates an infinity of detectors, out of which some number measure state A and some measure state B, such that the Born rule predictions by "counting" detectors).
This is the part that remains unexplained.
There is only 1 detector, and it, along with the detected particle, is in a superposition of states.
Again, this is where the language of "worlds" becomes misleading, and why I don't like it.
This is exactly the measurement problem, essentially identical between Copenhagen and MWI.