I gave it up after five/six years of use. However it was only really the last three I used it consistently. Once I left the abusive relationship I was in, I stopped. Going back to my parents away from the lifestyle I had there helped a lot.
At the time I didn't think it had any effects, however in hindsight I replaced it for alcohol and became dependant for a while on that. About six to nine months later I started doing weed again, however only occasionally. One tenner bag lasted me a month. Still drinking a lot.
A year, and too many bad-bordering-on-moronic decisions to name, later, I met DP online. He didn't like weed so I stopped it around him. Still drank and smoked cigerettes. Fell pregnant, moved in with him and stopped the lot. Harder to stop drinking than smoking weed but that was probably because I'd cut down massiely, and replaced it with booze; but it got easier as time went on, mixed in with my own stubborness not to give in :) Had my first glass of wine when DS was a week old. Went back to smoking cigarettes only after he was born.
Have had a few splits in the past year and a half since DS was born, the first last halloween and one six months ago when DP was battling cancer and my granny's dementia had reached the advanced stages. Both times I was staying with a friend overnight with DS at my mum's. It doesn't bother me anymore not having it or drinking much more than a few cans of fosters on a night time. But it took me a year and a half to feel this way. I know a lot of it was because I fell pregnant, which your EXDP wont do, obviously, but I think it would have happened eventually had I not, as DP was and is everything I've ever wanted and needed in a man and a relationship. It took me meeting him though to want to get better. I can't say this will be the same in your case, OP, not knowing you or your ex, but looking back it wasn't so cut and dry to just quit.
One week isn't anything, though like you said you didn't think he'd do it that long, so it's a start if nothing else, and everyone has to start somewhere. However weed very rarely causes issues. I myself smoked it to help me forget about my issues and feel calm. Giving up weed just made those issue more stark, if you like. This may be the case with your EXDP.
My advice would be to wait at least six months then see how he is doing with it. By then it will be out of his system, and he may or may not faced up to the issues he has. Be supportive, but stay strong to your convictions and stay away and look after yourself. It'll be the only way he'll seek help and change what needs to be changed. However also be prepared for him to possibly go back on to it when he realises your sticking to your guns.
My ex who I used to smoke it consistently with would never have put our relationship above the weed. Drugs do that. He made a lot of right noises but ultimately never really stopped. I never went back. Good luck OP. Really hope things work out for you.