Ask your students why this should happen? The mass has increased, but why does that change how it balances?
The water moves when the can tilts, causing the center of mass to shift – with just the right amount of water, the new center of mass will be above the edge of the can, and so it will balance.
Some cans will tend towards a particular orientation and will roll along the edge to that point, displaying a damped oscillation – invite students to hypothesize why this is.