real_username:
I think you're agonizing too much over making the "right" choice. What's true is, if you choose to forgive her and stay, the relationship will work... or it won't. If you choose to leave, or she leaves you, you'll find another relationship... or you won't. Life will go on. So I would try making the decision
based on what you want instead of what you "should" do, like there's an examiner sitting just out of sight, waiting to mark down your decision with a red pen.
There is nothing, fundamentally, that you can do to "make" her love you, make her stay with you, and make her stop cheating on you. Those decisions are out of your control; you have to accept that, for the moment and possibly forever, your girlfriend is someone who cheats on you.
Given that information, what do
you want to do? What decision will maximize your happiness? If you choose to stay, then you've made your decision. You've decided that the girl is worth it, and you don't get to whine about her cheating. If you choose to leave, then you've made your decision. You've decided that your pride is worth it, and you don't get to whine about the difficulties. Either way, once you've made the decision deep down, you can look her in the eye and know that it's really you telling her what you're doing, not fear of the moment or mindless bravado.
No one can make that decision but you. I don't think that staying is necessarily weak and spineless. It takes far more strength to love someone despite their faults than it does to walk away. But the
reason it takes strength is that their faults will hurt you -- and this fault will hurt you more than most. You have to know and accept that. If you can take on that pain for another's happiness, then kudos to you. But if you take on that pain simply out of fear (fear of losing her, fear that you're not good enough for a relationship, fear that you can't find someone else, fear that kicking her out will be too hard) then I'll have to go with the macho braggarts and say that you're a coward and a doormat.
Good luck either way. And, despite my harsh comments above, PM me if you want to whine.