When is 'heavy' used in callsign?
The rules are slightly different in different countries, but common for all is that the "heavy" designation is used for aircraft in the heavy wake turbulence category, that is, aircraft with a maximum takeoff mass of 136 tonnes or more (see Is there a definition of light/medium/heavy aircraft?).

Some countries require aircraft to use the heavy suffix to their callsign in all radio transmissions. Others only require it on initial contact with a new ATS sector, whereas others still will additionally require it to be used at all times in the aerodrome environment, but only on initial call in the en-route environment. The local rules will be listed in the AIP for the country in question.

Also note that in some places, certain aircraft types are considered to be in the heavy category, even though their MTOM is below 136 tonnes. The typical example of this is the Boeing 757, which is put in the heavy category by some countries because it creates significantly more wake turbulence that other aircraft with similar MTOM.