You have to understand, he was fighting with Anakin... When lightsabers clash whoever is the more powerful will eventually break through the others defence. That being said, Obi was exhausted because he was fighting with full power, and the heat didn't help things either.
Every swing was a homerun shot, otherwise, Anakin would of just broke through his defence and killed him. Lightsabers aren't weightless, the blade is, but the hilt is about 2 pounds or something like that. Swinging at full power though, anyone is bound to be tired. Especially clashing with someone as powerful as yourself.