Sure there is some funding, but believe a majority is paid for with fees and taxes.
The exact funding numbers, and the exact extent to which airports are controlled by the FAA, are supplied in the two links above. There is no point arguing. If you're under the impression that airports are an example of private enterprise, I suggest you review the two links I provided. If you already did, I suggest you do it again. Some things are not worth arguing about, especially when the facts are right in front of you, and this is one of them.
Why do you think this is an argument?
You need to read more carefully. There are a series of "if" statements in the above comment, along with some statements expressing my unwillingness to argue some points. Only you can say whether the "if" statements apply to you. Only you can say whether you will try to argue any of those points.