Collecting and reporting stories about cheating is an industry unto itself. Look at the sometimes factually-suspect TV show "Cheaters", or the rapidly rising website Cheaterville https://www.loveawake.com/free-online-dating/United-States/state-of-Maryland.html. But there are some downsides to outing cheaters publicly that are not so obvious, and if you're sitting on a ticking emotional time bomb, taking it to the television or the Internet is not necessarily the best thing to do.
1) The Person Cheated On Is Going To Be Humiliated
Cheating isn't something people get over easily. It isn't like slipping somebody a note and they can run off to the bathroom for a good cry and then they're over it. It's potentially something that could completely alter the course of their life, and will definitely put them through the emotional wringer.
And instead of keeping it their business, revealing the cheating in public makes it everyone's business. Everyone knows, everyone has an opinion, and everyone gets up in the cheated-on's face about what to do.
2) You Look Just a Little Bit Slimy
Here's a question that, if you out somebody as a cheater in public, will sit in the back of everyone's mind that knows you for the rest of your time with them: "Is he or she looking through my stuff to see if I'm doing something I shouldn't?" We all know busybodies and the like; it's part of living anywhere that there's always somebody who wants to make your business their business. Ask yourself: do you really want to seem like that person?
3) You Could Be Wrong
Then there's this: unless you've got video or something, in which case I've got to ask just what the heck it is that you do for a living, if you have no definitive proof, you could be slandering somebody who is completely innocent. That's a big risk, and it's bad for everybody involved if you're wrong.
So, how do you actually handle it? Three steps:
First, take the person aside privately. Make sure it's just you and them, no one else.
Secondly, lay out your concerns. Make it clear you're worried about the person.
Thirdly, don't discuss it with anybody else. Make sure the ball is in his or her court, and they can handle it the way they see fit. This does not mean, by the way, that you have to approve of how they handle it.