If you can have two of the same weapon class, and I don't see why you shouldn't be able to, then I most certainly will do so. Not all the time, of course, but I will do it. Especially dual sidearms.
Primary Weapon maximum size is based on your class. Lights can take Light weapons (SMGs confirmed, LRs currently unconfirmed, but implied), Mediums can take Medium weapons (Shotgun/AR), and Heavy weapons for Heavy bodies (Minigun, Grenade Launcher).
Secondary Weapon maximums are a step down from the Primary weapon, so lights can only take Pistols/Revolvers, while Heavies can take ARs and Shotguns.
But because you don't HAVE to take the largest weapon available, it's possible for a Heavy to have dual Machine Pistols (although it's unlikely to be the most practical thing to do).