There is certainly a connection to the castle, but this is not documented. The pond was certainly not given this name without reason.
Today, the Burgweiher is a fishing lake, partly covered with water lilies and classified by conservationists as a natural monument worthy of protection. On a hike along the Lieserpfad and the Eifelsteig in the direction of Wittlich, you will be able to view the Burgweiher from above. A descent and a stop in close proximity is worth the effort.