Most of us have felt the way you feel right now. I've spied on mine and felt like s*** afterwards. He's "cheated" (with his wife whom he was separated from at the time) on me too. Many women on here are married to the A's in their life. I, like you, am not.
No one can answer for you what you should do but I would suggest you keep reading the stories on here. It's helped open my eyes to what my future will be like if had I stayed with my exabf. Even my exabf's mom once told me "you don't need an alcoholic in your life". She loves her son dearly so I took that remark very seriously.
I've also read on here that it is dfficult to shake an alcoholic and I have come to find that to be true. They tend to be very needy. Something I still don't understand when it seems most times they just need anyone to be there to complain to. But I just thought I'd trhow this in because if he works for you it will be difficult to end your relationship.
I still love my exabf but I'm content to love him from a distance because I just can't live my life that way anymore. This is the way I'm dealing with it now.