In my feelings/ losing feelings

My bf and I have been together going on 3yrs. We have always had the same outlook, goals, and plans. We never really had any problems or arguments till I found out he was cheating on me. He did admit to it and has apologized. But has done it again and again and again and i think he is still doing it. Since the first day I found out, I felt so hurt. It made me want to throw-up. Sometimes thinking about it makes my stomach hurt. It really worsen my anxiety. We’ve been having problems with that since then and disagreement we have ends up about him cheating. He keeps saying he isn’t doing it but I don’t trust him. I want to leave but I also feel like I can’t. I have asked him to prove to me that he isn’t doing it by him showing me his phone and deleting girls off his Snapchat, Facebook and phone numbers but he says he won’t and that some of those are friends he’s known for a long time but also they have messed around before. We aren’t friends on any social media and he doesn’t have any pictures of me or us together. I no longer have Facebook after he blocked me and never added me on snap. We have had arguments and fights about it and he has threaten me with leaving. He has stayed a night or two at his sisters each time we argue. He keeps asking how long he has to prove that he isn’t cheating. I’ve told him until he shows me that he can delete those certain girls like I have deleted all my guy friends and gone as for as deleting my fb. On our last argument.. he said our relationship is pretty much day for day and doesn’t care for shit anymore like he use to. I do have proof that he was still cheating on me recently and it’s eating me inside. I look at him and all I see is hurt... but I also see love and I don’t want to leave. I can’t see myself without him. But I also know I shouldn’t be treated this way. I have backed off and he is noticing and he thinks that I’m up to something but I’m not. I don’t know if I starting to lose that feeling of caring and ready to let go or if I’m jus giving in to dealing with it and let it be jus to be with him. I feel it. I see it in myself. I don’t know what to do. I don’t know what’s worth more.. holding on or letting go.