He's getting a free flight using his frequent flyer miles. Airport tax is paid to the departure and arrivals airports. The airline collects this tax and pays it to the airports. Even if you are not paying for the flight you are still using the airports and you have to pay the tax. It's the same for everyone.

In my experience, the baggage limit on 'free' tickets is the same as that for paid-for tickets but you might have a higher limit if you have a higher grade of privilege card.