Fun and funny are different things. Having fun doesn't always follow with laughter so sentence number 1 doesn't create a cohesive thought in my mind. If you said however "I expected it to be funny, but it was way funnier than I anticipated" then you could definitely use that in certain contexts like the one in your title- for example, my friend wants to send me a funny meme- I expect it to be funny- but it was way funnier than I expected so I laughed harder than I should have at it. You laughed harder than you should have because you expected something less and were pleasantly surprised- thus bursting into laughter.
Otherwise in number 2
It just entails that you were placed in a situation that it was inappropriate to laugh, and you harder than you should have becomes a more negative descriptor of your action of "laughing".