Can the players pick up the weapons from killed enemies? Or would this cause too much imbalance if the weapon was not already included in the scenario?

Monsters don't have weapon cards, so there are no weapons for investigators to pick up. Technically, monsters don't use weapons (other than natural/unarmed), although fluff text on some of the humanoid cards will comment about using various items like staffs and such.

In other words, no, the investigators cannot "pick up" weapons from dead humanoid enemies. This is a boardgame and not an RPG.

Thanks for the input. That's what I was leaning towards...less RPG, more board game.