With the relative little progression I did I certainly noticed rain and wind hit some areas. It wasn't anything that affected game play really other than add realism or set mood.
The most interesting weather I did see was a regional affect (because it was a point of interest of some kind) the higher you went up a mountain. I was using Shadow Cloak repeatedly to more around an encampment of mobs to find areas to pull to. I went up the side of a mountain and suddenly the sky darkened, wind and rain started up and then lightning flashed and thunder hit so damn loud it literally scared me! I was only running the game at a very modest sound level but the thunder was so loud that is made my sub (set to low so not to annoy neighbors) pound so hard the room shook. The sound cracked so loud I thought real thunder had hit right near my place ... extremely rare to say the least as it is in the middle of snowy winter here.
I use a rather aged but still very decent Logitec 5.1 surround system with paired with a 5.1 Soundblaster card in my pc. It has a rather impressive sub too for the money I spent. The game does an excellent job of balancing sounds within reason (you can adjust of course with sliders). I always had serious issues in Swtor trying to hear voice conversations over regular sounds. I would need to turn down all other sounds to about 1/4 and still I could barely hear voice conversations over them. Swtor sound also never worked terribly well with my surround system. ESO worked nearly perfectly out the door.
I'd like to see if other types of weather are common in game too (including extreme) but at least it is paired nicely with great sound.