That's too bad about the bird. A chicken once decided to reside in a barn/garage like area at my parents house back when I lived with them. My sister decided to start feeding it a little food. After about two weeks, our dogs escaped from the field we kept in by running out of the gate while we were trying to get in. Why did they want out so badly? The chicken. In just a few moments, there wasn't anything but feathers left. The black lab we had essentially wolfed it down.
In the end, the reality is that dogs were bred to hunt. We had a sporting dog, and that's exactly what she did. My sister, though? She was really upset. I clicked the link. I clicked it because I was shocked to hear there was something left. Dogs are good at what they do.
I am curious, though: Did the bird always remain in its cage, or did you ever let it out and treat it a little more like a pet? If you did the latter, did the dog see that happen? It's possible the dog didn't realize Tweety was a pet, and he was just trying to get a snack he saw as a snack.