Well, using the stereotype is to reinforce their point. It's a argumentative tactic. Like if someone said "eating greasy McDonald's or whatever", they could have just said "eating unhealthy food" but using specific imagery that plays into stereotypes gives a more emotional reaction.
Maybe, I'm not sure where I fall on that. I view it basically the same as like the "fat American" stereotype- so is that xenophobic? Actually I would say that is worse, because being dainty isn't necessarily a negative trait to many people.
It was an analogy? I think you misunderstood what I was saying. I wasn't saying its not xenophobic, I was asking if you thought it was, and saying if you think it is then I agree it is consistent for you to then say that OP's statement was sexist. Not every discussion is an argument, don't be so defensive.