This is a newly placed outpost next to a rather new city:

Note how the outpost just completely ate away at the city's already established area of influence.

This is silly, imo.

A city should exert a stronger influence than an outpost, no? Or at least there could be some middle ground?

I've seen this behavior before, in which any newly placed object or upgrade which is able to affect influence completely overrides anything that was already established, without any middle ground or calculations on how strong the existing influence was. It feels like weak design and it doesn't make sense in the game world. For example, faction power could be used here to judge who will actually influence who.

EDIT: God damnit, FE! A turn later I look back and the borders have shrunk to normal... I guess this is again the same root problem as the number 10 item (and all subsequent) on my list from my first playthrough.