Yeah, kitchen scale tolerance is usually at least +/- 1 g which is equal or above the 1 g difference you give us. Not saying it isn't a fake though.
You might want to invest in a precision scale with +/- 0.01 g tolerance as well as a caliper (digital or old school) they are not exxpensive and should be in the repertoire of every collector. Also try to not touch the faces of a coin when you handle it.