The reason why they call this the bridge of sighs is not a very joyful story. It was the walkway to the dungeons under the palace and through those tiny windows there, the prisoners would have the last glance on the world out side before they would disappear into the dungeons for ever.
Despite the gloomy background story, the bridge it self is a most amazing piece of architecture, and when it's lit up as the sun goes down, it positively radiates.