Since the introduction of update 5.2, Mech Crusaders allows you to research for special research weapons. Research is done at the Research Center at the outskirts of Sector 3, and can be accessed via the sidebar.
Weapons research is split up in 4 different categories, with their own types of weapons. Research takes time, but doesn't cost anything otherwise. You can research all types of weapons, researching a specific type will not bar you from researching another later. However, as you research more weaponry, researching more weaponry will take increasingly more time.
There are 4 different branches available for weapon research.
Anti-matter weaponry is both deadly and expensive. Anti-matter reacts with armour plate and mech defensive structure with equal effectiveness and thus all anti-matter weapons ignore enemy armour values entirely. All anti-matter weaponry is unique, so you can't use more than one of each type.
Weapon module research is a new field which has progressed rapidly since weapon-merge technology became available. Modules are merged onto weapons to give those weapons their effects, so they cannot be equipped alone. Because of this, even though they are purchased just like other researched weapons, they do no damage at all.
Weapon systems that are designed to fit onto certain, specific mechs are destined to be extremely powerful to those who can wield them effectively. Some Integrated research goes towards strong weaponry, while others are just support systems that deal no damage but can benefit their team mates such as give group evasion. Beware though, these integrated weapons systems are unique and cannot be merged with other weapons or modules. Integrated weapons and items cannot be equipped within a Quad.
Experimental weapons are the oddball type of researched weaponry, as they can have special effects that can protect you or even give benefits to your whole squad. However, experimental weapons still have standard damage types and are all unique, and their cost can be prohibitive.
All anti-matter weaponry, all experimental weaponry, and all integrated weaponry have the 'unique' property. This means that you will never be able to equip two of the same weapons from these types at the same time. You can still equip multiple weapons from the same type as long as they are of different research tiers. Modules are never unique.