What does 亲你一口 mean?
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).