It is more correct to say "more and more fun."

Why do you go there? It's cheaper and funner, that's why. That was the funnest! The use of fun as an adjective is mainstream now, and -er and -est is becoming increasingly natural with time. It's a classic example of how small words evolve in English. That said, I wouldn't say there is ever a need to use them. That would upset a few people that you don't need to. In your example, in particular, "more and more fun" sounds smooth.

Funnier as an adjective does exist, with an i before the e. Funnier comes from the word funny and means that you can laugh about it. Funner exists as a synonym of more fun, and is sometimes used. I would not choose it and have never heard it in a conversation, though. More fun also exists. More fun means that a situation or activity is more enjoyable. Examples: We will go to Disneyland this summer. This will be more fun than just sitting in our garden doing nothing. Careful: "this is getting more and more fun" can also be used in a sarcastic way! Hope this helps

more fun

I agree with the other posts. If you're a native speaker and you say "funner and funner," it will sound like you're purposely using bad English, maybe as a joke or to be cute. If you have a foreign accent and you say it, though, it will sound like you don't know the language well.