This is a pun on 'away' which means to or at a distance from a particular place, person, or thing. But 'aweigh' is used in it's place because it sounds similar and it means (of an anchor) raised just clear of the sea or riverbed. On a news team, an anchor is someone who is generally a host of the program, but 'anchor' is also a device used on ships to plant themselves in place
The weekend reporter sailed through the newscasts while the anchor was aweigh .