Can you tell different iPad Configurations by their Weight?
According to Apple, the LTE version is 9 grams heavier than the WiFi version.

When you look at that picture of the logic board of the iPad Air (http://d3nevzfk7ii3be.cloudfront.net/igi/rqfMxwyBxWTko3xN.huge, taken from iFixit iPad Air 16 GB teardown, the yellow one is the Toshiba NAND Flash chip) you can see that there's not much room for more chips, so they would just integrate the same chip size with more NAND inside for e.g. 128 GB configuration. So I did some research about that and it seems there are up to 128 GB chips in the same size since 2010/2011 (just that time Apple first released a 128 GB model, what a coincidence :D). So theoretically this would be possible. Of course, you'd need to see a teardown of a larger model to say for sure.

Having said that it'd be hard to tell the difference in weight between those configurations, independent if they put more NAND in one chip or used maybe 2 chips for larger configurations (what looks difficult if you take a look at the layout of the motherboard: http://www.ifixit.com/Teardown/iPad+Air+Teardown/18907). The difference would be just below 1 gram...