I always thought it was referencing beauty and the beast. Cause the same things happen in beauty and the beast. In Aladdin it's not a spell. It's just a genie with magic. In beauty and the beast it's actually a spell on the castle.
Lilo was so passionate about Pudge the fish's happiness and well being because he supposedly "controls the weather". Her parents died because of bad weather, and she never wants that to happen again to Nani or herself. And my heart just broke.