My recollection from the news accounts of the SwissAir crash was that the term "heavy" was used to indicate that the aircraft was carrying significant fuel.

In the case of the SwissAir flight, which had just taken off from JFK and had enough for the onward flight to Zurich(?), it declared an emergency at referred to itself as SwissAir xxx "heavy".

At least that's what the New York Times put in its annotation to the transcript.