what parameters must a flight meet to be called "heavy"?

A 'Heavy' is an aircraft capable of takeoff of more than 255,000 lbs.

When talking to air traffic controllers, pilots will add the term Heavy to the end of the flight call sign on flights involving very large aircraft. For example you might hear this : "United 341, heavy, ready for departure". This term alerts air-traffic controllers that they need to provide extra spacing between aircraft as these aircraft generate significant wake turbulence which can disrupt the flight path of the aircraft right behind. The term is typically used around airports as that is where the cause for concern of wake-turbulence is highest. Some typical aircraft that use this call sign are the DC-10, B-747 and B-777. Of special note here is the B-757 which even though might not strictly qualify as a 'heavy' from the weight point of view, is still treated as a 'heavy' by air-traffic controllers as it is notorious for its wake-turbulence generating properties due to the specific nature of its wing design.

Maximum gross takeoff weight greater than 255,000 pounds.

This designation applies regardless of whether the aircraft is actually loaded to 255,000 pounds or not (i.e. its still a heavy when its empty).

Examples are: 757, 767, 747, A340, A380, MD-11, and quite a few more.

Randy B stole my answer . . . curse you!