I had a neighbor who smoked in the apartment below us. We didn't have kids then, but my husband had asthma that was getting much worse due to the smoke coming up through the floor. I actually did try to respectfully talk to him, but he told me to f off. But he also had a serious drinking problem and no job, so there was a lot going on there.
You could try to talk to your neighbor--but you do run the risk of him then switching from smoking on the balcony to smoking in his place, which as another poster mentioned, would be worse. If you talk to him about it, he *may* start to smoke outside, away from the building. But what about next winter--is he going to keep that up when the weather gets cold?
I would definitely get a good air filter--I can't remember where we got ours--qvc.com I think. You can find ones that filter out most of the particles and chemicals in smoke.
You didn't mention your child's age, but if the filter isn't enough, you could think about switching your child's room with the living room, or some other room (if you have an office, playroom, spare room, etc.) Or, move your child into your room, crib only. I know those aren't ideal solutions, but if it's only temporary, and your child's health is the consideration, you might want to consider it.