I currently carry a Nikon FE film camera around when I want a camera small enough to forget about, but I am itching to get an X100F in particular.
I traded it all in for a fuji, and 2 small primes, and I bring that camera everywhere.
If you need reach and magnification, for example at an airshow, then you need a long lens with a lot of glass. At that point the weight of the camera becomes irrelevant.
If you just need a couple of primes for street shooting then just about any camera manufacturer will sell you something small and lightweight. Fuji don't have any particular light-attracting or gravity-defeating magic.
Also can't wait till all apps are phone independent. Right now most third party apps stop working without a phone.
The apps I'm waiting for are Car2Go or Uber that work totally independently. Also, unfortunately, Google Hangout for work.
While I'm making wishes, it'd be amazing if I could sync with my MBP instead of my iPhone.
Sony's current compact line seems OK, though I haven't used them--the DSCWX cameras. They've got Exmor sensors (their mirrorlesses all use Exmor sensors) and reasonable lenses. You won't get mirrorless performance, but you're not expecting to, so, yeah.
I get my messages, my calls, and my emails. I can get directions if necessary. I even get my wallet, my weather, my reminders/schedule AND my music. What else do I need?
EDIT: Did I mention it also tells time?