For those that don’t know, they are sometimes pronounced the exact same, which is why they are often mixed up (see also affect and effect). Where I’m from weary is pronounced WEER-y though.
Not true (at least in the US): weary (at least the adjective) is pronounced with a "we" at the beginning, while wary is pronounced with a "wear" at the beginning.
I hear "weary" spoken so very rarely that I have no idea how it's pronounced here (Indiana). I can't even make up my mind how I pronounce it, but I'd wager it's almost, but not quite, indistinguishable from wary.
Of course it varies with accent and locale. So phonetic transcriptions don't help unless we use IPA. But in British English, "weary" has a diphthong and "wary" does not. Very distinctly different words.
On the subject, we pronounce "router" and "router" (two different words, same spelling) differently, one with a diphthong, one without.
Yes...ish. That's the correct pronunciation, but neither are used frequently enough for me to be confident that's the actual pronunciation, and I'd wager it's different in different places.