I know many here would say since you are inviting you need to pay for everything... I look at it a little differently.
If you can afford it, then pay for everything except extra souvenirs. However, if you really can't afford the extra cost, offer the trip to the friend's parents before saying anything to the friend, and let them know the costs up front. If they want the friend to go they can pay for the costs. I would still pay for the meals.
We've taken my children's friends on many trips, and if I couldn't afford the extra child I would have no problem proposing the trip & costs to the parents. (However, I've never gone on a trip where we couldn't afford to pay for the child)
If my child was invited, I would expect to pay airfare and tickets to the themeparks, etc., and be grateful that he/she had the opportunity to participate in the adventure.
Whatever you decide to do, just let everyone know ahead of time what is expected.