If you are speaking of the divisions in weapon rank such as Crude to Legendary, then the answer is that there is no affect.
The distinction of a "Famed" weapon from a "Rare" weapon, "Legendary" from "Famed," and so forth, only acts a generalization as to how hard it is to find the weapon, and the overall strength of the weapon in comparison to the entire artillery that is available in the game. However, just because a weapon is a Famed weapon does not make it automatically stronger than all rare weapons - in contrast, there are many rare weapons out there that are much stronger than some Famed, or even Legendary weapons.
In reality, the "rank" of a weapon is simply meant to show how hard it is to find the weapon, and to make the card look really nice and shiny. Other than that, there is no programmed strength difference for a generalization of a specific weapon rank.
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