[SAI_Peregrinus]

Infinite "yous" does not follow from an infinite universe unless one adds a constraint on the distribution of matter in that universe. E.g. one could have a finite observable universe that we see, then an infinite expanse of cheese. No extra "you", unless you're cheese. Infinite does not imply random.

[skirmish]

But if I observe a Shroedinger's cat after opening the box every morning, I do get at least duplicated. Repeat this lots of times, and MWI says there are for sure 2^n copies of me as the lowest estimate.

Counting all daily QM-influenced events everybody experiences (a cosmic ray either passed through me or decayed before it reached me, a radon atom either decayed in the air right next to me or not when I went to my cellar etc.), I think it is fair to say there are nearly infinite copies of you in various multiverse branches (of course, some who collected lots of radioactive decay events are already dead from cancer by now).

[n4r9]

If you observe the position of a system whose quantum wavefunction has non-zero probability over a non-empty interval, then according to MWI would you not create an uncountable infinity of duplicates of yourself?

Arguably this would be limited by the reporting accuracy of your equipment, but perhaps the thought experiment can be tweaked to get around that...