I know ratting is the worst sin you can commit for lots of people but in his case I don't blame him. Michael used him. He got what he needed from Tweener, knowing full well he'd never repay him. Tweener got raped daily by Avocado because he stole the watch for Michael. And while Michael does let Tweener in on the escape plan, that was Tweener's worst option at the time. Why risk getting caught and spending an extra 10 years in prison, or possibly killed, and being on the run the rest of your life, when you can get protection and time off your sentence that isn't too long anyways?
If Michael hadn't used Tweener like he did and didn't cause Tweener's trouble, I'd think him ratting on the escape was unforgivable. But with the way Michael treated him, I don't blame him.
Back in season 1, Michael was using absolutely everyone in Fox River besides Lincoln - remember, it was originally just supposed to be him, Lincoln, Abruzzi and Sucre who escaped and he probably initially had plans for Abruzzi (and Sucre before he got to be friends with him) to be recaptured fairly quickly afterwards; every extra person that got added to the plan was a potential liability. And while I don't necessarily blame Tweener for snitching, I do think that he brought quite a bit of trouble on himself. He antagonised a lot of people when he first arrived by trying to act tougher than he clearly was, and (to put it bluntly) being a white boy trying to attach himself to the POCs. And Michael actually went out of his way to try and protect Tweener a few times, particularly from T-Bag. Bellick was more responsible for what happened to Tweener than Michael was: he's the one who backed Tweener into a corner and forced him to become a spy for him in the first place and then put him with Avocado when he didn't come through and sided with Michael.
As for why Michael was so cold to Tweener after he found out, like I said, every extra person in on the escape was already a potential liability. But at least the rest of them, for all their various issues with each other, ultimately cared too much about getting out themselves to tell anyone else or to truly risk endangering the plan (except for T-Bag and Michael tried to cut him loose several times too). Michael really only cared about getting Lincoln out of Fox River and Tweener had significantly jeopardised that. To be honest, I don't think we're ever meant to think that Tweener snitching was unforgivable, it's more tragic than anything. He was caught between a rock and a hard place and tried to pick the best of a group of bad options - at the same time, we know Michael's got a very good reason for being angry at him. Tweener's entire storyline on the show is essentially one tragedy after another.
When did he play both sides until he was being threatened by Bellick. He helped Michael by stealing the watch. Not only did Michael do NOTHING for him in return, but it got him in trouble with Bellick. Thats not playing both sides. Thats trying not to get killed by a psychotic correctional officer.
Tweener wanted to get in on PI which was something Michael at that point in time could definitely not afford to do because Michael had already determined that there were already too many people in the escape crew.