Theoretically, it's not infinite because of the granularity of time/space, speed of light, and so on.

(Nitpick: Spacetime isn't quantized AFAIK in standard physics, and then there are still continuous quantum amplitudes.)

This, I think, is what Wei meant when he said we couldn't just give equal weights to all possible universes - the ones where the coin lands on heads and the ones where it lands on tails. But I think "universes where the coin lands on heads" and "universes where the coin lands on tails" are unnatural categories.

I thought Wei was talking about single worlds (whatever those may be), not sets of worlds. Applied to sets of worlds, this seems correct.