Question
is there a type of weed barrier that can be put down underneath lawn?  We have created a path up our hillside and there are oak and maple growing everywhere and I want to know how to keep the trees from growing up in the middle of the grass

Answer
I have not heard of a weed barrier placed under turf but that does not mean that it cannot be done. Whether it is going to be effective in your case is another matter. Acorns and other seeds falling on top of the weed barrier will germinate and root through it anyway.