This ultra-lightweight (~3kb initial load, ~7kb with weather data and gzip enabled) weather web-app lets you check the current weather conditions anywhere in the world. It works with and without javascript and does not have any dependencies other than the weather api.
http://pat-mc.com/projects/10k-weather/
The weather data is provided by a free api from openweathermap.org. To get an API key go to http://openweathermap.org/appid and sign up for free. Once you have a key, edit the first line of scripts.js:
var wxAppId = "3XAMPLK3YW1THL3TT3RSANDNUMB3RS";
Weather icons are by Adam Whitcroft and are optimized using SVGOMG.