Getting Twitter to work with your Raspberry Pi Pywws powered weather station is relatively straightforward, when you know how of course. The main thing is that there are some additional dependencies you need to install.
First, install python-pip (see for example http://www.pip-installer.org/en/latest/installing.html#install-or-upgrade-pip):
sudo apt-get install python-pip
Then install the things that you need for Python Twittering:
sudo pip install python-twitter
Now you should have all the software you need, so assuming that you already have a Twitter account follow the guide here:
http://jim-easterbrook.github.io/pywws/doc/en/html/guides/twitter.html.When it comes to the authorisation part:
python -m pywws.TwitterAuth /data/weather
you will need to do some copy and pasting to your browser, the keys should be automatically copied to your weather.ini file.