I've noticed something that I think is fun. Or maybe funny. Let me explain.
Somebody can say that something is 'fun' and mean that it's a source of amusement or enjoyment. This applies to both humorous and non-humorous situations. The word 'funny' has the same connotation, but here humor definitely has to be involved.
This makes you wonder why the diminutive form is there for humor. Both fun and funny can be applied to a longer period of time (playing game can be fun, a show or a person can be funny), so it probably isn't because humor and laughter more often depend on the impulsiveness of the moment.
Maybe the diminutive form is a sign of tenderness. In order to feel more close to others, we give them diminutive forms of (nick)names. On the other hand, making things smaller could be a sign of nonchalance. 'Funny' could be a kind of peripheral area of the much larger and more significant domain of having fun. Just like 'risky,' 'thirsty' and 'moody' are peripheral areas of the much larger significant domains of taking risks, having a thirst or having a mood. Now the diminutive form suddenly is a sign that humor is not to be taken too seriously or maybe even that it has little to contribute to our lives.
In some ways, however, funny has more nuances than fun. You can, for example, use inflections like 'funnier' or 'funniest,' while you can't say that yesterday was 'funner' than the day before or that you think watching sports is the 'funnest' thing of all.
Maybe this only shows there is more of a competition in humor. Maybe it shows the usage of these words should be carefully researched in the future and be compared to words words with similar word forms and their meanings in other languages. Most probable of all is that me talking about these issues doesn't prove or solve a thing.