This is my experience bringing a miniature poodle into the States when I moved back in 2002.
I had all my papers translated. I did the move in 2 phases, with two days layover in Paris. Last phase was CDG
. No one weighed the dog. Having said that you need to have the dog fit in the carrier of the right size . It helped that he was quiet and not barking.
When I arrived, I said to the official at immigration, I have a dog, would you like to see the papers? She said no, that's OK
, maybe at customs. When I offered to show the papers at customs, and said, I have a dog, they said, "that's nice lady. Welcome back". And that was it.
So my suggestion is to get Eddie as close to 8KG as possible -- the limit on many carriers -- and make sure he is happy in his correctly-sized carrier.
Then see if they can fly from CDG
which would save a half-hour off flight time. In my experience the European carriers are more pet-friendly.