I must have missed that memo...

When did "big" become interchangable with "old"? I always thought "big" referred to size, not age.
And yet I have conversations like the one I had this morning..

Her: I'm calling to find out how much it'll cost to spay two dogs.
Me: Well, it depends on how big they are.
Her: One's just a stray that showed up, I don't know how old she is.
Me: That's ok, how much does she weigh?
Her: Well, I really don't know.
Me: Alright, our prices vary with weight, so it'll be somewhere around $100, more if she's over 50 pounds, and a little less if she's under 25 pounds.
Her: And what about the other one? I've got two, so how much will it cost to spay the other one too?
Me: It'll depend on how big she is.
Her: Well, she's only 5 or 6 months old
Me: That's fine, but some breeds get much bigger than others and as I've said, the price varies with weight...do you know how big she is?
Her: Well, not very, I mean she's only 5 or 6 months old.
Me: (Argh!) Yes, you said that. But age doesn't change the price. That's by weight.
Her: Oh, ok. So will she be less than the other dog? because she's younger.
Me: (Holy hell woman! would you fucking LISTEN TO WHAT I'M SAYING?!) It'll be around $100 for each dog, depending on how much they weigh.