If you start the quest, A Night to Remember (the Sam Guinevere drinking game) at night, then when you enter Markarth, the Forsworn Conspiracy will not trigger properly; Weylin will not attack Margaret.
However, I did find a workaround for PC: go to the merchant stalls during the day, and type these console commands: "Prid 9C8AB" and "Setrelationshiprank -4". This will cause Weylin to attack. It won't be a backstab instant kill as normal, but it will trigger the quest once Weylin is dead.