I've not played it yet but have read the setup and cards. It says to set aside the weaknesses at the start of the game. Why do you do this? When do they come into play? Many thanks.

They never get into play. You can earn them because of the campaign (just like prof. Rice and the Necronomicon).

Which is fortunate, because putting a Weakness in play almost always means you get it permanently added to your deck.

Quote

If a weakness is added to a player’s deck, hand, or threat area during the play of a scenario, that weakness remains a part of that investigator’s deck for the rest of the campaign. (Unless it is removed from the campaign by a card ability or scenario resolution.)

From the FAQ. This one is added to a player's deck as part of a resolution, anyway.