From my read of the “Twitter Files” I hey have multiple levels of ways to reduce a tweets reach. Not allowing a tweet to trend, not show up in Search etc. I believe the “heavy” part refers to how many, and how hard these levers are pulled.

I think this is the first public occurrence of this term. Supposedly there are couples more that are independently named by users.

Mea culpa! I've edited my comment to fix this.

("visibility filtering")

VF = Visibility Filtering = "Shadow Banning"

Thanks, seri4l!