Nowadays, those two words are pronounced the same by most speakers, although many English speakers in some regions of the US (particularly in the southeast) still maintain the more conservative pronunciation of the WH — as a whispered W. You would recognize it if you heard it, because the sound is similar to a very quick Japanese “FU” sound. I imagine the WH sound will disappear entirely in another generation (sadly).

yes, but in UK has some difference http://dictionary.cambridge.org/dictionary/english/whether

They are pronounced the same unfortunately. Whether is used when you are showing that two alternatives are possible. (ex: I don't know whether John wants to eat pie or cake) Weather is used in place of 天気 to describe what it's like outside Hope this helped

Thanks for the information about Scotland, and for mentioning you occasionally use the WH yourself. Believe it or not, I’m really happy to know that. Since the H in WH corresponds to a Q in Latin, I believe it is particularly interesting for fans of Grimm’s Law. As far as the US, I believe the challenge lies in the fact that Hollywood and New York media are so dominant and so “cool.” As an aside, your description of being “taught this sound by elderly schoolmistresses” matches what I’ve heard from people who grew up in NYC half a century ago.

It depends on your accent. In Scotland, these words ARE pronounced differently : 'whether' has a short breathy 'hoo' sound before the 'w' in Scots pronunciation, whereas 'weather' doesn't. And until fairly recently, this was also considered the correct pronunciation in RP English - I was even taught this sound by elderly schoolmistresses when I was at school! Today, though, for most native speakers they are the same. I only use the 'wh' pronunciation if I want to distinguish between two words such as 'which' and 'witch'.