There is not a logic reason why ちょっと is written often as チョッと, and things become more complicated when you can find around 3 different ways as

さかな - 魚 - サカナ

きれい - 綺麗 - キレイ

おしゃれなかばん - お洒落な鞄 - オシャレなカバン

it depends on what kind of effect the writer need to comunciate, what kind of feeling he inted to pass.

we can roughly identify a few typical feelings conveyed by these 3 types of writing:

・Kanji →classic, hard, heavy, difficult, serious, reliable, etc.

・hiragana → easy , light , soft , childish, simple etc.

・Katakana　→　 fashionable, smart, impressive, new

Hiragana, being round, gives a soft impression while Katakana is made of strait lines has a cooler impression. I think this is why you see it often in advertizements (ads want to draw attention using katakana)。

My image of チョッと待ってis the quick movement of an arm trying to stop someone and ちょっと待って is more like a pat on the shoulder. 

You wouldn see チョット because と is a particle and shouldn't be written in katakana.

I never write チョッと (because I think ちょっと looks better) but I think the sound+と style is popular in Japanese. For example,サッと炒める、グッとくる、キラッと光る、ギュッと抱きしめる。