I personally don't think it has to do with distortion, down-tuning, or mixing.
There is a reason classical music sounds like a range of different moods and emotions, and that same idea is often carried over in heavier music. Its the same reason that Tool, while not being heavy metal, sounds heavy. Adam Jones's writing for guitar makes use of note choices and chord combinations that evince a certain kind of response.
The same principle is present in every single genre, not even just metal. A song could be written in guitar tuning of one whole step up, but if you write the parts accordingly, it could be described as 'heavy.'
Kyuss's desert/stoner rock sound is really thick, C standard tuning. But, Josh Homme uses the same C tuning in Queens of the Stone Age as he did in Kyuss, and No One Knows sounds remarkably more upbeat than, say, Demon Cleaner.
That being said, distortion and other effects serve to embellish the original sound. It doesn't define the weight the song carries so much as it magnifies the intent of the song.
This is purely subjective though, because everyone has different definitions of heavy. When I was a kid, a Slayer fan teased me for saying SOAD was heavy. At the time, SOAD was like listening to lead because no other music I had listened to prior to them had that emotional intent. Nowadays, I can throw on Acid Bath and jam out because I've heard a huge range and interpretations of "heavy" music.
It's the emotional intent you write the song with. Writing happy music will sound happy. Writing angry music will probably sounds angry, and what's angry now might not be as angry in a few years.