No extra fee. Carry on bags need to be small enough to fit through a standard xray machine like they have at airports. And you have to keep your carry on bags with you until the staterooms are ready at 1:30 so don't carry on more than you can lug around with you until then.
There's no size or amount restrictions for the bags checked with the porters, but I would still try to keep weight of any one individual bag close to the 50 lb limit set by airlines. Why? Because a big part of the reason for the limit is to make it safer for the baggage handlers who need to lift the bags. The heavier the bags, the more likely they are to cause back strains and other injuries. So be kind to the baggage handlers and yourself and try not to pack bags that are way over that weight.