As it turns out, I found the original Weather Station library a little too convoluted to work with. It works great with the intended screen size (128×64), but although it's possible to support additional geometries, my initial steps into the rabbit hole made me rethink my strategy.
You see, Daniel's Weather Station library includes custom versions of more established libraries for performing tasks such as displaying text and images on the screen (all hail U8g2!), parsing JSON, etc. And so, I decided to start from scratch, building a GUI on top of the widely adopted U8g2 and a web client for the Weather Underground service suing the built-in ESP8266 http client functionality on top of the ArduinoJSON libraries.
So far so good, more details coming soon!