There was a regular who posted here (NoVAPlantguy) who grew a river birch on his balcony. You just have to do pruning to maintain whatever height you feel you can handle. The river birch is just hardy to Zone 4 so it would be very marginal on your balcony without some protection if it gets extremely cold though. Usually a good rule of thumb is to look for plants hardy to 1 - 2 Zones lower than your own for container growing. This makes it easier as you wouldn't have to jump through alot of hoops to protect them in winter while containerized.