I'm gonna play devil's advocate just for a minute here, despite having just said I think this was stupid. But this is at least a little better than a girl being won over and becoming a weak ineffectual mess by being called beautiful, which we've seen variations of in One Piece before. Mainly because Sanji has been fawning over her for ages now, and she's reflected 100% of it. It's not just a "womanly weakness" moment I don't think. Or at least, not too severe of one.
If we take the flashbacks at face value, unflinching acceptance of the third eye is probably enough to indeed give her pause. This is the first person in her life to give her this kind of validation, but I think the exact circumstances of the moment probably play into the severity of her response. If Sanji had said this to her elsewhere, I bet she'd be shook, but maybe not collapse-in-a-fit shook. Because right now she's having to process this while literally SECONDS away from having planned to blow his fucking brains out, with everyone watching expecting it to happen. It's a short-circuiting of expectations, she can't just process it at her own pace, she has to process it AND fight with the fact that she's expected to be killing him right this instant.
It was supposed to be so easy to just kill him right then and there, and then he had to go and do that. It's not just tears from "oh man he's validating my fundamental flaw," it's ALSO tears from "why now, why does this have to become difficult at the last second."