There are rarity levels for the weapons in the game, I am wondering how much of a difference there is in damage between the rarity for each weapon?
Rarity actually has a very strong effect on weapon power. Whitesushii, Reddit's resident Fortnite guru, has put together a spreadsheet here that goes over a whole bunch of stats - not just weapon damage, but hero strength, traps, survivors, skills, the whole shebang.
He's also done more in-depth analysis specifically on rarity's effect on weapons. In his Reddit thread here, he discusses the differences in DPS and durability between rare, epic, and legendary schematics. He even tries to account for perk rolls, which are hard to measure accurately due to the RNG that goes into generating them. His conclusion is that the difference in damage values between epic and legendary weapons isn't too bad (less than 20% difference, or about one white/blue perk's worth of value), but the gap between rare and legendary is very large (greater than 40% difference).
Though he only tested with one "set" of assault rifles, the power levels are probably similar for other weapon sets as well.