What do you think that fat guy did to get him in prison?

I think he did something particularly heinous. Rape/murder. But because he is a full fledged psychopath he really believes he didn't belong there. And his beating/death showed Andy that no matter how hard you try to explain yourself, nobody there gives a crap about you or your story.

*We* are the music makers... and *we* are the dreamers of dreams. -Willy Wonka

The prison was for felons, so his crime had to be serious

He didn't seem the type to commit murder. Possibilities include -- sex with a minor, drug crime, thefts, embezzlement, forgery, perjury

He had a pedo vibe to him. Definitely reminds me of somebody who would be told by Chris Hansen to have a seat.

He was innocnent so he didn't do anything.
He might have been mistakenly sentenced.
Maybe even framed.
But he stated quite clearly:
"Im not supposed to be here. There's been a mistake".

Everybody in Shawshank is innocent, didn't you know that?

At first he was real thin.
Then when he was afraid of getting caught he ate all the evidence while shoplifting everything in a grocery store.

Lawyer f*ked him

Burglary or selling drugs.