You can think of data like wifi but through a service provider like telus,rogers, etc.
Those small data charges could have indeed come from your phone updating your weather. If you don't want data, you can disable it in your phone settings. Just keep in mind that you won't be able to send picture messages when data is disabled.
Hopefully that helped. :)
You can also contact Koodo and have them place a data block on your account sotthat nomatter what you do data can not be used and thus you won't acure any charges. Keep in mind that you won't be able to send or recieve picture messages if data is blocked like John stated.
Apps use data as well as widgets or weather so if you use any apps those may be using data which you may be able to check in your settings menu under data usage, Android gives you rundown list of what is taking data so you will knowbby checking there.