love=pain (like the name btw) I will address your question under the assumption that you want an honest answer "pure vulcan logic" as it where and not a "shoulder to cry on" type of response to make you feel better about your decision to reconcile. So if I am incorrect in that assumption please simply skip over my inane ramblings
and ignore me.
As to my answer, I think it depends on who or better yet where you ask the question, for instance very few men that decided to stay with a wife that cheated on them are gonna come out and say "Yep i'm just a big ol' sissy for staying with her."
Having said that, I do believe a lot of people, even a suprisingly large amount of women tend to view betrayed men who stay as being weak or passive. I don't have any statistics off hand to back that as it is merely an observation I've made from my own life experiences and discussing the topic with others.
Most people on this forum, being made up largely of betrayed spouses and former cheaters don't seem to feel that it makes themselves or their husbands "beta" or if they do they are not very likely to say that here, what with their spouse reading the screen behind them.
However when the topic has come up in casual conversation in "real life", I have generally heard negative things said about guys who took back their cheating wives. Usually it pertains to an assumed sexual inadequacy or the man is casually referred to as a "chump" or other such hurtful suppositions are made about his "manhood" both figuratively and literally.
Not knowing a whole lot about biology I can't really give you a physiological reason for why so many women seem to be attracted to "alpha/bad boy" types. You would have to PM Machiavelli for that.
I personally think it at least partially a societal/environment issue and not completely genetic. For instance younger girls have traditionally obsessed over boys who could barely be descried as male at all let alone "alpha", just look at Justin Bieber. How do they explain that?
I don't feel that it necessarily makes one less of a man to reconcile, in fact I would go so far to say that a man staying with a truly repentant wife could even be an example of GOD's mercy and love that is freely offered to all of us. I don't know what spiritual beliefs(if any) you hold but in the OT of the Bible GOD describes himself multiple times in the terms of a betrayed husband with an unfaithful bride(Israel), whom he longed to forgive and be reconciled with if she would only repent of her (spiritual)adultery and return to HIM. So there is at least in my view a righteous way of reconciling that is inspiring in it's mercy, humility and forgiveness. But it is most certainly not for everybody. And you do have every right legally, morally and even biblically to divorce her if you so decide.
I won't whitewash the facts, from a purely societal point of view a man taking back his adulterous wife is largely considered to be undignified. As far as I know, it has always been that way and it's not likely to change any time soon. I guess what it comes down to is can a man still be happy/content with his wife and marriage knowing that others (family/friends/co-workers) may think less of him for taking her back? I suppose that is something that each individual must decide for himself. And it only adds another layer of how vile adultery truly is and what destruction it leaves in it's path. Whatever you decide I say good luck to you.