I did a bunch of testing on watch towers last night.

It appears that a city when it's first built has no sight range besides the exact square it is on. The next turn when it has a 1 square influence range it can then see 5 squares away. It appears that city sight range is thus influence +4.

Building a watchtower has no visible effect. There's a couple of reasons that I can see that would cause this.

1. Watchtower does not currently increase sight range at all.

2. Watchtower does increase the sight range but influence sight range instantly is larger than watchtower because the bonus is applied directly to the city square, and doesn't affect the influence sight range.

How to fix?

I would suggest a couple things actually. Reduce city sight range to be equal to the influence. Being unable to see beyond that (Without additional units with greater sight range), And then having watchtower apply it's bonus to the vision from the influence.

This way a city can see it's immediate vicinity, units with sight range boosts can increase that lending them use, and the watchtower can give a scaling boost based upon city size.

Caveat: All of the above assumes that I understand what is going on with the watchtowers, but I don't know modding/XML so I can't delve into the issue.