I'm going to look at my ex-girlfriend's facebook messages
Why would you read her messages?
Because I want to see what she's been up to.
What is the point of reading them? You should not get hung up on the past relationships of your partners.
I will do it for fun.
Even if it's for fun, it's still a bit weird to read your ex's private messages. You should probably just leave her alone and move on from her.