This is gonna sound more rude than intended, so pardon the unsmooth language. It is not meant to make you sound stupid, wrong or anything else, it just makes it easier for me to get my point across, so again i ask your forgiveness in advance, and please don't take anything personal.
I find the question slightly confusing, do you want to become okay with it? or are you looking for justifications for feeling troubled by it?
I'm gonna assume it's the first, for the sake of the post, since i can't give you a halfway decent answer to the second option.
You list all the reasons why you shouldn't be bothered by it, stating a lot of points peopel usually use to justify their smoking of weed, i'd do so myself, if i was put in a position where people didn't just accept it.
Heres gonna come some assumptions, if they don't hold, just ignore them. They might apply to others and not you.
You say you're okay with alcohol and ciggarets, but not weed. This might be because weed is not legal like the others, making it sortof a hard stance to take, to object to those things, whereas weed is easier to object at because it's illegal, so you have the "public stance" to back you up in your oppinions. If you have secret dislike for people drinking or smoking tobacco, this is probably into the reason.
You don't smoke weed yourself, so you might not like the way people get when smoking weed, i know for instance that i'm not the most exciting company when i'm high. But then again, you should tell people that they're dull to be around when they're high, and not bother bothering about what the do, when you're not around.
Perhaps You don't like your girlfriend smoking weed, because it's something you can't relate to yourself, and you have some kind of controll freak mindset, that makes you want her to assimilate, and become more like you, because you're afraid of you and her beeing too different or something like that. Just like some people will insist that videogames is retarded, immature and a complete waste of time, totally ignoring the facts that it makes you happy, and can quite often benefit you otherwise as well, when they keep telling you to give them up, and grow up.
Perhaps you were born and raised with the idea of the law beeing something that should be blindly obbeyed, and even though you can see why can be less harmfull/bad han alcohol, you can't get past the point that it's illegal, even if you consider the law stupid. Just like people getting butthurt if they see someone walk over a lightcross when the light is red, just cause there was no cars around.
Perhaps you've been fed too much anti-weed propagande through your school or other places, and can't rid your head of the idea that it is inherently evil, despite your logic saying otherwise.
Perhaps you're justifiably afraid of the legal consequences for her, seeing how it is illegal, and purche and possession of weed can lead to sentences if caught (i don't know what kind of sentences in your country, they're minor where i live, if you're not selling)
If she could face serious legal trouble for it, i can fully understand your concern, despite the actual crime beeing victimless.
Perhaps you're afraid to pull back on your innitial stance, cause it'll make you feel like you "lost" the argument, or that you'd have to admitt you were wrong. Politicians are famous for this, they'd often choose to appear stubborn and stupid rather than admit a mistake. This could possibly apply here as well.
Perhaps it's something completely different, but if you can use anything written above, feel free to tweak it to apply more to you, and if not, remember that this is guesswork from a stranger online, so don't feel judged, or anything like that.
Cheers