our girl is 1 and we have traveled with her playpen and car seat several times from Doha (to europe three times and asia once).

in our experience the airlines are quite nice when you travel with a baby, and weight has not once been a concern. on 2 of the above trips, the person checking in next to us was charged for extra weight (they were not traveling with a baby).

the only downside is the playpen nylon was slightly damaged on one trip (but nothing major).