I was hoping someone with better info could get back to you. I fly with my birds sometimes, but size/weight for them is rather irrelevant to you.
There is a max weight allowed, I think it's 15lb, and I've never had them weigh my carrier, so I think they'll take your word for it.
Like everything else, they are more strict than they used to be. Make sure you have reservations, they have rules about the number and types of pets allowed. with my birds, I've been bumped because someone showed up with a cat before I got there, and they don't allow "incompatible" pets in the same cabin (they also don't allow the pets out of the carriers, so I'm not sure how that's relevant).
I agree with your DH, I'd rather have a dog cramped in a too-small crate then put in cargo.