It's sort of in-between. BST has been grouped with heavy (both Delve sets, lol Ebon sets) and medium (Salvage, add-on final rewards). With the sphere bodies, it gets both the heavy and medium ones, much like how PUP gets medium and light sphere bodies.

If we had to list the jobs by armor class it would probably look something like
WAR/PLD/DRK
DRG
SAM
BST
NIN
THF/RNG/COR/DNC/RUN
MNK
BLU
PUP
RDM
BRD
WHM/BLM/SMN/SCH/GEO

Good point about the Dynamis procs. From what I can tell, they generally considered BST heavy during original/RotZ era (Adaberk), then medium in CoP through Lv99, and now they're more often heavy in iLv era.