A Weekly Event is is an event that lasts a full week and then resets. The Arena is the only true weekly event, starting over every week.
Doggy, Giant Knight and Kraken events are bi-weekly on a rotation. One of the three events starts every other week in a specific order, starting with Kraken, then Giant Knight, and finally Doggy, before starting over again with Kraken. These events also last a full week once begun.