I love
Eve. It is so elegant in its simplicity.
I don't see it at all as a "saddling" type of name. I don't see how it would be at all a burden to bear. It has no negative connotation that I know of. It's not something that would invite teasing or ridicule, so I don't see a problem with a child named
Eve.
I don't think
Eve as a middle name is a cop out, as
Rose,
Mae,
Leigh,
Grace are. Like them, it sounds good as a middle name with most first names, barring one-syllable ones, but it's not overly used as a middle name and not fillerish, that I'm aware of.
Susannah Eve is gorgeous.