I’ve had the same thing happen to me but only since the latest release (5.6.12).
It only happens with the skinned tooltips and seems to be related to right-clicking on the WW icon in the tray (and choosing Options… if it matters).
The tooltip then becomes permanent and changing active cities will pop the new correct tooltip on top of the old one!
Seems this didn’t do it for me at least…
I wasn’t able to recreate it using the right-click as before but I did manage to recreate the permanent skinned tooltip by timing it just right using the left-click (configured to open Weather Watcher).