The AV means "centre weighted averaging" - it averages the reading over the scene, with extra weight given to the centre.
SP means spot, and it is indeed responsive to a moderately large central area - about what you describe. It is difficult to describe that area exactly, because the description varies with different screens. I find I can see where the sensitivity falls off on the screen if I carefully move the camera side to side and up and down while looking at a small light source.
The Auto A-S measures both AV and SP readings and automatically chooses one or the other, based on an algorithm that tends to favour a spot reading when the two diverge.
One thing I note with my AE Prism finder N is that it is susceptible to battery inconsistencies. Are you using silver oxide batteries?
Are you sure you haven't set some unexpected exposure compensation on the finder?
The system depends on setting the film speed on the back, and having that information communicated through the camera. You might check that the meter responds correctly when you adjust the film speed.
I'd also recommend cleaning the various electrical contacts.