I've been working on this for a time (a statistician's hobby) and here's what I think is going on with weight:
The level of variation is about plus or minus 10% for a particular model. Say for a 20" Medium Ride the median weight is 2250g. That means the expected weight variation goes from around 2025g to 2475g. Once you get outside that range you are more likely looking at a model with a lower target weight (eg crash ride, thin, crash, paper thin, etc) or a higher target weight (eg medium heavy, heavy, rock ride, etc)
The 10% is an early (and rounded up) estimate based on
[LIST]
[*]current target weight ranges published by Zildjian (thank you Paul Francis)
[*]vintage weight ranges (occasional cymbals with ink intact)
[*]current weight ranges where the model and weight class ink is intact
[/LIST]
The reason we experience more variation in older cymbals (particularly 1960s and earlier) is that we're mixing up different models because the model ink is long gone. In another recent thread I reported on weights for 18" Avedis Zildjian cymbals with model and weight class ink intact and this gives the flavor of the number of models and variation we're dealing with:
http://www.vintagedrumforum.com/showthread.php?t=60539
Then to make matters of interpretation more complex, the target weights for something like a 20" Medium Ride also changed over the decades. The targets got heavier (going from 40s and early 50s vs later 50s then 60s, 70s, 80s) and then were reset in 2013 for the A Zildjian series back to the 60s.
As far as sound goes for a given diameter: weight has a role and so does the curvature of the bow (higher curvature = holding more tension = higher pitch), and the size and shape of the bell (the bell radiates the higher frequencies), and the degree of taper (metal getting thinner towards the outer edge). These parameters all interact and there are others in the mix as well. I rely on my cymbal maker friends to help me with cymbal morphology and sound. I'm just the numbers guy.