With all due respect, I would suggest that you consider what types of ramifications your actions are going to have on your wife's trust issues and self-esteem when this affair is finally exposed.  Oh, and believe me when I type the truth that your indescretions will eventually be exposed, whether you're still involved, or not. 

Before you engaged in your extramarital activities, did you ever speak to your wife about engaging in couples' counseling?  Did you ever approach your wife about her emotional unavailbility and how it affected you before you had your fling?  Exactly how is your wife "emotionally unavailable?"  And, who initiated this affair and under what circumstances? 

I'm not reading one shred of remorse about how your actions and choices will affect someone with whom you have entered into a legal, binding contract of marriage with.  This is all about you and how this is going to impact her is cleanly and thoroughly dismissed as a complete aside.  "I don't want to let it go," instead of, "I don't know how this is going to destroy my wife."  You're suggesting that you wife is unappealing to you because, suddenly, you feel attractive and that you somehow deserve whatever it is that you want and unless (and, until) your wife follows suit by losing weight, you won't be able to see beyond the scale to the person that you married.

If the desire to maintain a relationship based upon truth, honesty, and open communication has simply died, then the relationship is doomed and no amount of weight that your wife loses is going to alter this fact.  Nothing that she says or does is going to change this. 

This may come off harsh, but it's truth:  it may be best to put an end to a charade while you both still have an opportunity to rebuild your lives in a healthy manner by divorcing.  From personal experience, it is far more difficult to "pretend" as time goes on, and once you're on the market, again, you can enjoy whatever sexua| interests that you have with as many various individuals as you wish. 

Either way, I would suggest that you seriously consider telling your wife about your choices so that she, at least, can review her options and get tested for any STD's that you may have passed to her that you may have picked up from your "girlfriend."  Seriously.  Be a grownup about this and part ways amicably so that you can both rebuild your lives.