There's nothing much you can do OP.
He's entitled to smoke. I don't think whether he's a tenant or an owner matters, I don't really see that as being your business as other posters have suggested. Even if he does have a no smoking term in his contract, you don't know if it includes the balcony and, even if it does, they'll likely do an inspection and if he's being careful not to let smoke get in the flat, they'll likely find nothing to complain about. You just risk creating a hostile relationship.
You COULD report him for the weed, he's technically committing a crime but, in reality, the police aren't going to care unless he's secretly running a weed farm. Even if they do show up, there's little chance of any consequences and, as a smoker, he'll know that. Even if a knock from the police does make him stop smoking weed, he'll probably just smoke more cigarettes to compensate.
Your only real option is to casually mention it to him and ask if there's anything he can do to avoid/minimise the impact on you. If he says no, he says no. Hopefully, even if he says no, he'll be decent enough not to take offence.
Are your balconies adjoining? The other solution I can think of (if it's a big enough problem for you) is to put an extractor/fan on your balcony that he can reach. You could explain the situation and ask if he wouldn't mind switching that on while he's smoking. You'd probably want to explore the options first before actually doing that in case he say's no and you've wasted money. I don't know how much that would help with the problem? Would a fan/extractor work? You never know, he might even offer to contribute - I would as an ex-smoker who always tried to be considerate but that's just me.
It's a shit that the burden of finding a solution is on you but there isn't much you can do otherwise. It's the downside of communal living.