From tallship technology, the constant verse ".. up she rises" naturally depicts weighing anchor, from when it breaks free of the bottom through complete weighing, when it's no longer in the water (none of it buoyed, its full weight hanging from the hawser): "Weigh, hey and up she rises..". The chanty would seem to have particular (original?) use to accompany the hands at the bars as they push the capstan 'round.