Weigh anchor means to lift the anchor off the seabed and secure it for sailing. This term is synonymous with preparing to leave or starting a voyage:

Process: Weighing anchor involves not just the physical lifting of the anchor but also ensuring that it is properly stowed and that the ship is ready to make headway.
Significance: The phrase is often used metaphorically to mean embarking on a new endeavor or moving forward in one’s endeavors.

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