what with... 是口语习语。意为 “因为；由于”，表示原因和理由。后面接名词性词组，或动名词（包括含有逻辑主语的动名词复合结构）。例如：

What with one thing and another, it was fairly late in the day when we returned to Shrewsbury 

（由于）忙完这个又忙那个，等到我们回到什鲁斯伯里的时候，天色已经很晚了。

《柯林斯高阶英汉双解学习词典》

What with the heavy rain and his not knowing the way, he was late.

（因为）下着大雨，再加道儿不熟，所以他迟到了。

《汉英大词典》

Maybe they are tired, what with all the sleep they're losing staying up night after night 

也许他们是太累了，考虑到他们成宿成宿地熬夜。

《柯林斯高阶英汉双解学习词典》

She lives very far away, and what with transport problems, she seldom comes. 

她住处离这里远，加上交通不便，所以很少来。

What with teaching and what with writing, my time is wholly taken up.

一是因忙于教课，二是因忙于写作，我的全部时间都被占去了。

网友的句子是疑问句，这时，what with...可以翻译成 why...？

me slipping you a finger —— 动名词，含有逻辑主语的动名词复合结构。

You know, what with me slipping you a finger? 

你知道，为什么我暗中帮你?