Why does a bucket of Water weigh more than a bucket of Air?

It was actually just that, a bucket full of ice cubes. I did explain that a large portion of the ice bucket's volume will be air to my friend. He is starting to agree but is also posing the question of "If ice and water weigh the same, then why does ice float?." But I am a little stuck on how to give a good example to compare the question too.