The Etymology of Nitwit

I love the term nitwit. I love what it means and I love how it sounds. From dictionary.com:

nitwit

A stupid or silly person.

Now I grew up believing that nitwit was closely related to nitpicking, that both terms were about nits.

nit

The egg or young of a parasitic insect, such as a louse.

That is, I thought the term nitpicking came from picking nits, which, louse being very small and their eggs being even smaller, well, you get the idea. Now I was suprised to find the etymology of nitwit on dictionary.com makes no reference to nits as in louse eggs but instead attributes it to the German word for nothin, nit or niht. The story is the same for nitpicking, which is apprently about picking 'nothing'. I find that less than satisfactory and wonder if there is some connection between the German word for nothing and louse eggs.