On MW, there are an infinite number of worlds at time t if an infinite number of quantum outcomes has occurred by time t. Anyway, it sounds like you're thinking this: There are an infinite number of worlds. A quantum event happens in many of them. There are more worlds where it happens than where it doesn't. Therefore this event is more likely.
But that's not MW. MW says that something happens, and when it happens, you get one world for each outcome. There's a problem here because what these outcomes are depend on the basis you write the wave function in, but that's a different issue. It's certainly not saying that there are an infinite number of worlds, each with a determined series of events, and we have probabilities because some of those worlds are more numerous than others. That's modal realism, as I said in a comment above.
By the way, that doesn't just raise its head in the context of quantum mechanics. It only does because it gives us reason to believe that it's physically possible that things could've been different than they actually are. But it seems possible-period that things could've been different, even if physics was deterministic. Even though it might've been physically determined that I went to the grocery store yesterday, it's certainly possible tout court that the whole universe had gone differently, and I could've gone to Fenway to see the Sox game instead. But does that mean that there's an alternate universe where my otherworldly counterpart went to Fenway? Isn't there a simpler explanation for why that's possible? QM has alternatives, like the Bohmian and GRW theories, which are far more plausible as well.
But that's not MW. MW says that something happens, and when it happens, you get one world for each outcome. There's a problem here because what these outcomes are depend on the basis you write the wave function in, but that's a different issue. It's certainly not saying that there are an infinite number of worlds, each with a determined series of events, and we have probabilities because some of those worlds are more numerous than others. That's modal realism, as I said in a comment above.
By the way, that doesn't just raise its head in the context of quantum mechanics. It only does because it gives us reason to believe that it's physically possible that things could've been different than they actually are. But it seems possible-period that things could've been different, even if physics was deterministic. Even though it might've been physically determined that I went to the grocery store yesterday, it's certainly possible tout court that the whole universe had gone differently, and I could've gone to Fenway to see the Sox game instead. But does that mean that there's an alternate universe where my otherworldly counterpart went to Fenway? Isn't there a simpler explanation for why that's possible? QM has alternatives, like the Bohmian and GRW theories, which are far more plausible as well.