In a double battle, if a Pokémon uses Snatch, than you activate the Weakness Policy, do you steal the boost or can you only steal moves like Sword Dance or Nasty Plot?
No, you would not steal the boost of Weakness Policy
Source: Experience with Snatch and Bulbapedia and all other sources I found, all of them say "Steals the effects of the next move the target uses." Weakness Policy is not a move.