How to genetically classify a mineral resulted from weathering?
My understanding of supergene is that it is about mineral enrichment/concentration at the base of an oxidized zone, within a weathered profile. The seasonal/periodic rise and fall of the local water table is critical to supergene enrichment.


  The descending meteoric waters oxidize the primary (hypogene) sulfide ore minerals and redistribute the metallic ore elements. Supergene enrichment occurs at the base of the oxidized portion of an ore deposit.


Supergene would not apply to the top of a weathered zone but to the base.

My old geology dictionary (The Penguin Dictionary of Geology, 1979) describes supergene as:


  A word suggesting an origin literally 'from above'. It is used almost
  exclusively for processes involving water, with or without dissolved
  material, percolating down from the surface. Typical supergene
  processes are solution, hydration, oxidation, deposition from
  solution, reactions of ions in solution with ions in existing minerals.


To me, supergene has a specific meaning, it may be part of the weathering process in some locations, but weathering involves the breaking down of rocks due to: reactions with atmospheric gasses, water (usually rain), changes brought on by plants, bacteria wind and temperature.

My suggestion to use the term weathering or weathered.