Luckily, in Mass Effect 3 any class can carry whichever and however many weapon types they want. Major changes have been made in the Heavy Weapons category: now you are not allowed to equip your character with them and they can only be found as pickups during missions.
Of course, it has a great number of unique guns but lots of them can also be found in the previous titles. Mass Effect 3 weapon system is an expended variant of the weapon system coming from Mass Effect and Mass Effect 2.
Weapons Guide: Assault Rifles and Explosives