Wow, this is totally interesting. I have tio think about this, I love it!

Ok- totally just thinking out loud (you know what I mean), you could have the centerpieces in varying colors (but maybe the same look to keep them cohesive, varied roses or tulips?) and have different names for the tables?

something like -

Grey for the “rainy day”

Yellow for 'sunshine”

Blue – clear skies

white – snow

there's got to be more.

Maybe you can do something with the Greek Gods of like Thunder (are there more for other weather patterns?)

How about crazy things like tornado and lightning inspired? those shapes seem like they would be really fun to play with.

My husband is a meteorologist. When we got married back in February, we incorporated weather into the reception by naming all of our tables after clouds and other weather phenomena (Stratus, Cumulus, Arcus, Graupel, Microburst were a few of the names we used). I would be happy to show you pictures of our table cards. 

We also incorporated a photograph of a Kansas tornado onto the chocolate groom's cake. 

Some meteorologist friends of his married last summer and gave away miniature tornadoes in bottles for favors. 

If you wanted to carry the theme further, I think it would be possible to rig cloud-like decorations to hang from the ceiling, perhaps using the Martha Stewart tissue paper poofs in groupings to give a cloud-like effect. 

You could also carry a graphic interpretation of the weather motif throughout your printed materials – using a simple line drawing of a cloud – or even using the official meteorological symbols for different events (I designed a t-shirt using the symbols for thunderstorm with hail that have been popular with my husband and his friends) and carrying this icon throughout your invitation, programs, etc.