I believe that on Everett's approach, when you measure some observable with two possible outcomes, the total number of worlds increases, like a bacterium dividing. But on the version you're suggesting, it sounds like we constantly hop from one already-existing universe to another, because every instant brings with it a different configuration. But it makes little sense for our bodies to hop between worlds, since they're parts of worlds, so is it our 'mind' that does it? But that sounds like many-minds, except with many worlds instead of one, and with a new problem of how we do the hopping.
Unless by configuration, you mean that each world is a world-line that contains a set of definite outcomes for all quantum events, and so all the quantum outcomes are predetermined for each world, and we explain probabilities by recourse to the proportion of some worlds to others. That's not really many-worlds, that's modal realism (every possible world exists, and "the actual world" just means "my world"). Which is more David Lewis than Hugh Everett.
In Everett's approach, I think it is the macroscopic state which splits. But the macroscopic state is a volume of worlds. So I guess think of the interval [0,1] as consisting of a single (macroscopic) world. But [0,1] has infinitely many numbers in it; each one comprises a different "world".
Under evolution, [0,1] splits into [-0.5,0] U (0.5,1], two macroscopic states but still infinitely many microscopic ones. Every state in [0,0.5] was turned into a state in [-0.5, 0] and similarly (0.5,1] -> [0.5,1]. (Each real number corresponds to a world configuration.)
(note: there are quite a few variants of many worlds, and not everyone realizes they are talking about different theories. I don't know if I'm describing the most common view. )
My (non-mainstream) mental picture of MW is bohmian mechanics, with each possible bohmian trajectory corresponding to a different world history.
>Every state in [0,0.5] was turned into a state in [-0.5, 0] and similarly (0.5,1] -> [0.5,1].
I hadn't heard this version, but it doesn't make sense to me. So these microscopic worlds each change when a quantum event occurs? If they can change, then why not think that there's only one world, which changes when you measure something? It's a lot simpler and seems to handle everything that this theory does. Of course, if they don't change, then we're in a microscopic world with a precise configuration at any given moment, and every observable has a value, and Einstein was right, and we wouldn't observe Bell's inequalities. But we do, and anyway, the whole reason we postulate this stuff is because we think that things in our world (you know, the one I'm sitting in, microscopic or otherwise) actually evolve according to the wave function.
BTW, if your picture is Bohmian mechanics, then you only need one world, where every particle has a well-defined position all the time, and these evolve according to the wave function. These different possible histories are epistemically possible because we don't know what region of the wave function the particle currently inhabits. But that's not a continuous infinity of worlds, microscopic or otherwise, unless you're just using the word "world" that way.
Unless by configuration, you mean that each world is a world-line that contains a set of definite outcomes for all quantum events, and so all the quantum outcomes are predetermined for each world, and we explain probabilities by recourse to the proportion of some worlds to others. That's not really many-worlds, that's modal realism (every possible world exists, and "the actual world" just means "my world"). Which is more David Lewis than Hugh Everett.