The rule book doesn't say anything specifically about this (or I'm just missing it). Does anyone know if an investigator can carry more than one weapon and if so, do you choose which weapon you're attacking with during your turn?
From the Attack Action section on page 9:
Attacking a monster is a common action investigators perform. The player selects one of his weapon or attack Spell cards and chooses a monster as dictated on the card. Alternatively, an investigator may attack a monster in his space using his bare hands.
So an investigator is allowed to possess multiple weapon cards.
There are as far as I know no rules regarding how many weapons you can carry and you can choose which one you want to use. There are though cards that will limit how much you can carry.
This had never really been a problem in my games though since the investigators usually are happy to even have one weapon let alone two.