A question about buffering and filtering a sensor output
The cutoff frequency of your filter is dependent on the input value of the vane, because it forms part of the source impedance of your circuit. If you want a well controlled cutoff frequency, put the filter after the amp.

I would also use a much bigger capacitor -- 100 uF/16V or higher are cheap and plentiful, and I don't think you have a space problem where an electrolytic cap would be in the way?

Btw, if the weathervane source impedance is 5k, and the filter resistance value is 1.1 kOhm, and you use a 1 uF capacitor, the RC time constant is 6.1 ms (about 1/164 second) but the filter frequency is about 26 Hz. However, when the vane is at the top, the source impedance is 1.2 kOhm, and at the bottom, it's 1.1 kOhm and the frequency adjusts accordingly (Just draw out the resistances as a ladder and this should become clear.)

Finally, if you're worried about high voltage build-up from static charge and from "random outdoors electromagnetics" when running a long cable, you could add a Zener or other TVS across the input terminals. That won't help if you get hit by lightning, but there are many smaller scale problems that can be avoided by doing so.