Illustrator - weaved effect?

Hmm..can you elaborate on that a bit?

Not having used the knife tool before, I don't really know what functions it serves.. would I have to split up the initial path into different sections in order to be able to cut it at the exact points?

Had a quick play around, and a quick Google, but can't make head nor tail of it.. :\
Hmmm. . . I use the knife like I would a real scalpel and cut the line where I want to. The best way is to play around with it and see what you can do.
There's about a million ways to do that particular shape, the knife tool mentioned above being one. If you look at the shape, it's actually only 3 lines.

So in this particular case, you could get away with drawing the top 'eye shape', using the pen tool.
Then, change the stroke weight to make it a thicker line. Then, go to path/object/outline stroke. You'll then be able to play with the nodes individually.
So you have the top shape, all you have to do now, is duplicate it twice then lay down the bottom two.