I've found a lot of versions, like:
- baffled why
- baffled about why
- baffled at why
- baffled by why
- baffled as to why
- baffled on why
- baffled over why
Is there a correct form? Is any of the above wrong?
All OP's alternatives are acceptable except on (over isn't good, but it's not totally invalid to me).
I myself am baffled by the etymology of baffle, which seems to have originally meant disgrace, thence through mock to the modern sense of to bewilder, perplex. I also think we tend to use the "passive" past participle more today - we say "He's baffled by it", rather than "It baffles him".