NoBadMojo has made the key comment, which is that the leather grips compress less. That can make them feel less comfortable to people used to synthetics but, on the plus side, they, unlike synthetics, hold the grip size .
As to the weight difference well, roughly (very roughly as I did this on a very cheap pair of scales but it gives you some idea), a ProKennex sythetic replacement grip weighed in at -roughly- 0.5oz. A Prince leather weighed in at just under 1 oz and a Babolat leather was just over the 1 oz mark.
Even allowing for my crappy scales (analogue) that does give you an idea of the weight increase when you go to leather. Also gives you an idea of how much weight you can lose if your racquet originally came with a leather grip (my POG mid minus the leather grip and plus a synth replacement is now (again roughly) a touch over 11.5 ounces.
In terms of the size difference between one leather grip and another, well, personally, that's something Im sensitive to but probably wouldnt be an issue for others.