is my relationship broken ?

I've been dating my boyfriend for a year and I love him so much and we took each other's virginities. He has had a very bad problem with weed to the point where he was doing it everyday and it was affecting our relationship. It got so bad his parents almost wanted to send him to rehab (were 19 if you're wondering) but he did not go and promised me would stay sober. I told him if he ever smoked weed again we would be done because I can't handle that type of addiction within a relationship. Two months later, he has smoked weed twice. Behind my back. Lied straight to my face multiple times because he said he was scared he would loose me if he told me the truth...I feel so broken and like I've just been cheated on. He's been having sex with me and going on dates with me acting like he loves me while lying to me about this ? I feel like I don't know I can trust him anymore or if I should stay in this relationship? Someone please give me advice on what I should do...