Heavy is kind of an arbitrary title. I dont particularly define it in any way, as I only use the term "Heavy Metal" explaining to people who dont listen to metal to say what I listen to.
That being said, I still consider certain bands "heavier" than others. Namely those with clear, but low riffs, who make the bass move, who blow out your speakers, who shred your ear drums (yet still have a very much musical ability)
Listen to Gojira (all three albums, but "From Mars to Sirius" specifically), Cryptopsy (any album, "None So Vile" and "Whisper Supremacy" track 6 for good examples) , Fear Factory (Album Soul of a New Machine, Demanufacture and Obsolete, especially "Edgecrusher" on Obsolete), see also the album "Chaosphere" by Meshuggah and anything by Vader.
Lots of stuff would qualify as "heavy" its all in what you are looking for. (A side note, I dont care what anyone else says, Flo of Cryptopsy and Tomas Haake are probably the best drummers walking the planet at the present, if you are looking for "heavy" drummers)
If you are looking for straight up deep subwoofer crushing noise, well, you could go with Mortician, or really, any other band out of the NY death metal scene