You would be hard pressed to get a special by-law approved on the basis that in a six unit block you normally need a special resolution to be passed by all remaining owners, no doubt the “offending” owner wouldn’t support it. The situation becomes worse for you if a poll were to be demanded, if the other units had a greater unit entitlement value than yours. Also I don’t believe that you would get much support in a tribunal over a tree blocking your view, even though views are highly sought after and contribute to the value of your unit.
What would concern me is that the trees may have been placed without regard to the load bearing capacity of the balcony. They could be quite heavy when fully grown (including weight of soil, the pot containing it and the tree itself).
There have been many well publicised cases of balcony collapse in recent years, many of these involved heavy loadings though usually of people, and deterioiation of the balcony through corrosion. Might be better to pursue those aspects through Fair Trading and possibly the Tribunal, safety issues should elicit a more sympathetic hearing.