Are there any restrictions to the number of weapons a survivor can equip?
There are no limits to the number of weapons that a survivor can equip and the effects stack. This has been confirmed in the Dead of Winter Rules forum on BoardGameGeek by Jon Gilmour, one of the designers of Dead of Winter.

Click here to read one of these threads (Jon Gilmour's responses are posted under the user name JonnyRotten). 

A second thread reference can be found here.