Why the dramatic name? This is the spot where sailors used to say goodbye to their loved ones, moments before sailing away for long periods of time. One of the famous expiditions that sailed from here was Henry Hudson, who discovered Hudson Bay in Canada, and a river in New York named after him today.
Truth is, if you check the translation of the name in Dutch, the name's meaning is "sharp corner," but it is understood as the Weeper's Tower.
Today there is a cafe and a club with jazz music in the tower.