It's been running in this configuration for a little while now. It works well, but the inaccuracy of the servo is just terrible. It seems pretty random how much overshoot there is so the unpredictability is difficult to manage in software.

Options to improve this are:

1) Try a better servo ($$)
2) Move encoder to the needle and add a control loop
3) Use a stepper motor.

Really good servos are expensive, and from my research, I'm not convinced they'll have the necessary accuracy. Adding an encoder to the needle could be done - either the one from inside the servo and use the servo's control loop, or add another one around the whole thing. Possible, but I think this is a bit messy.

So, going for option 3). I'm going to use the Switek X27.168 steppers designed for car gauges (Thanks to Adam for pointing these out in the comments).

Somehow, I need to physically connect the shaft to the needle. Not sure how to do this yet.

Also, someone parked a ship in front of the weather station I was using for data. It's still working, but unsurprisingly, the ship affects the reported windspeed somewhat. Given how hard it's gone aground I think it'll take a few weeks to move it.http://www.bbc.co.uk/news/uk-england-hampshire-30677320