The New Yorker has a famously idiosyncratic style guide that calls for diaresis to be explicitly marked (in words like e.g. coöperate). This is pretty interesting though because it seems to indicate that the pronunciation has shifted - nobody would pronounce "aero" with a diaresis today.

It hasn't disappeared in British (and related) English.

What is called an 'airplane' in US English is an 'aeroplane' in British English. Ditto 'aerofoil', etc.

'Aero' is a Greek prefix pertaining to 'flight'. (And also to 'air')

The two dots above a letter indicate that the two vowels are pronounced separately, rather than as one sound. As also seen in "The first Noël the ......", etc.