Credibility
First, I'm glad you've asked this question and I'm hoping this answer can not only help you but someone else in your position. Plus, to give this answer an ounce of credibility I'll have to give you some background into what I know, what I would have wanted (even at the time) and some further reading to help you devise a plan of your own.
Alcohol isn't fun when taken beyond moderation. Trust me I know, I worked in bars full-time for 6 years and throughout that time I'd progressively got worse and worse to the point where I was turning up to work or uni drunk on a daily basis. Even when I did morning shifts, just to help with the hangover. "Hair of the dog" was my favourite hangover cure.
Throughout that time, I had lost a few friends and a girlfriend on the way, even then I knew I was bad with alcohol but I didn't recognise I was an alcoholic. "I'm just having fun" was a classic excuse I'd use to worried friends (which is probably why he offers you some, because he thinks it's fun. Though you don't), even when they carried me home, I still had no clue the impact my actions had, I would then repeat the same thing the next day. I always saw it as a recreational habit, "I can cut down anytime"; something I thought I could control. But, by the end of it all, it controlled me. Safe to say now though I've been clean for about 4 months. But, less about me. Let's see what you can do to help your friend.
The help I would have wanted
In my opinion, the worst thing you can do for him is to detach yourself, I know it's hard to keep him around like this. But clearly, he needs people like you in his life. It's all about routine, he's stuck in a routine of habitual drinking and it's a hard cycle to break out of. but he won't do that until he recognises he has a problem.
You see him once a week, which is a great start. I would consider you to be good friends.
Keep a diary
I would have loved for someone to do this for me.
- First, get a notebook (an A5 one will do).
- Write a letter (it should be at the very front) to him at the very beginning stating your concerns and how much his friendship means to you and how you want to help him out, so he doesn't feel attacked and if he does he can take it home to read. (only mention it from your perspective alone, if your boyfriend doesn't want to get involved. Don't involve him)
- In the pages ahead, write a diary from what you can remember of when he's been at yours or around you that concerned you. Take note of the date, how much you thought he drank and what he did that night that concerned you (i.e. pass out so he couldn't go home as an example). Do not use any negative undertones. Be as compassionate as you can be when writing this out, he may read this over and over in the future. It'll be a hard pill for him to swallow but he'll know in the end, he needs it.
One-to-one
This is where the diary will come in handy. You now have ammo to back-up how much you want to help and how much you care. Be as patient as you can with him, it'll be a lot to take in.
- Sit him down (sober) without your boyfriend anywhere to be seen if possible.
- Hand him over the diary and tell him how hard it is to do this and that you want to help as much as possible to help him get back on his feet.
- If he feels attacked, give him space and emphasise that you want him to consider it and you're there, whenever he needs you.
- If he's willing to talk about it, ask him how he's feeling. Use some advice from PhyschologyToday where possible.
- Devise a plan (i.e. keep a log of how much he drinks and see if theirs any improvement over weeks). You can't expect him to go cold turkey. It took me a year of cutting down to finally stop. Or maybe accept he doesn't stop fully, just limits himself. Whatever you come up with, just let him know you'll be there to help him along the way and to keep an eye on him.
Only do this when you feel comfortable, but as you've said in your question you won't be able to take it much longer. You're more than within your rights to put a drinking ban when in your house after you've done this, if it'll help him. But again I'll emphasise, be as patient as you can. It's a long journey ahead. I commend you for wanting to reach out and offer a helping hand.
Helpful tips
You know him better than I do and if you think he won't react positively to what I suggested above. Then I'll give you some further reading if you want to come up with your own plan.