Relevantly for the LO/CB discussion, if Torn-T isn't banned, Weavile needs either a CB or to run Ice Punch.
252Atk Life Orb Weavile (Neutral) Ice Shard vs 4HP/0Def Tornadus Therian (Neutral): 66% - 78% (198 - 234 HP). Guaranteed 2HKO.
252Atk Choice Band Weavile (Neutral) Ice Shard vs 4HP/0Def Tornadus Therian (Neutral): 74% - 88% (224 - 266 HP). Guaranteed 2HKO.
LO Ice Shard rarely kills even with rocks, CB Ice Shard almost always does. Of course sometimes you will pursuit if you think it'll switch out, but not being able to back that decision up with a kill is pretty bad.