We were away friday-monday last weekend and i took cloth with me. I also took an extra large wet bag for the mucky nappies and washed them once i got home
We didnt fly though, just a 3 hour trip in the car so not sure how you would get round the baggage allowance bit.
Are you taking a buggy in the hold? If you have a buggy bag you can stash quite alot in there and it doesnt get weighed