If I attach focusout event on the $(window) and $(document), each events are called twice.
I use jQuery v3.4.1 and I have the same problem with Firefox (v74.0.1) and Chrome (v80.0.3987.163).
If I use native Js, each events are called once.
https://jsbin.com/rilamarodi/1/edit?html,css,js,output
open console, focus input field and go out (remove focus) to see on console that each events are called twice.

Thanks for the report. To add to that, on Firefox if I focus the input & then either focus another application or Firefox DevTools, I see 4 occurrences of the document focusout & 5 of window focusout.
I initially thought it's related to the big refactor of focus event handling in #4279 but the issue is even in 3.0.0.
but the issue is even in 3.0.0.
in 2.2.4 too !
OK, so this issue first occurred in jQuery 1.11.0/2.1.0. It was working fine in 2.0.3. It was introduced in 1cecf64e5aa415367a7dae0b55c2dd17b591442d. That commit broke focusout handling on non-element targets, though, a fix was added in c2aca17d457d302cb1683f925b9e5ee93f0984ea so that's the first commit where you can see this issue.
The issue doesn't exist on master which is future jQuery 4.0.0 because we removed the focusin/focusout shim there in PR #4362. We didn't backport the removal to the 3.x line as it changes the relative order between focusin/focusout & focus/blur events.
Taking into account that:
If you find a simple patch fixing the current 3.x implementation, we'd review the PR, though.
Marking for discussion at today's team meeting.
Oh, actually this is pretty simple: the doc variable in https://github.com/jquery/jquery/blob/3.4.1/src/event/focusin.js#L30 will match document for document & window for window and we'd like them to be grouped by document. A fix incoming, it will be quite simple.
That also explains why this was unreported so long - the issue happens only if you attach the focusout (or focusin) handler on both window & document, or on window & another regular node.
PR: #4656
Fixed via #4656, landed in 9e15d6b469556eccfa607c5ecf53b20c84529125.