What does 亲你一口 mean? I thought 亲你一口 means “kiss you” but usually, I think verbs take 一下 to add the meaning of “a bit”. 

So why is it 亲你一口, not 亲你一下, and what does it differ from just say 亲你? Or is the relationship between 亲你 and 亲你一口 the same as between 看你 and 看你一下?
亲你一口 and 亲你一下 mean the same, kiss one time. 口 and 下 are both valid measure words for 亲. So, 亲一口 == 亲一下. 

You should note that 一下 doesn't ALWAYS mean 'a bit'. It can mean 'one time'. For example, 打三下（hit three times）， 亲两下(kiss two times).