Landscaping fabric without mulch?
We have a side hill that's really overgrown with weeds. It's about 10 feet tall by 100 feet long and maybe 30 degrees steep. About twice a year I go and pull out or cut down all the trees that have sprouted, usually a dozen or two, between 1 and 4 feet tall. But this is really a hassle because the entire hill is overgrown with poison ivy; even when I go and cut/pull trees at the very end of winter, long before the poison starts growing, I still get the rash on my skin.
I've had a couple landscaping companies tell me it would be thousands of dollars to clear the hill and get something like ground cover planted... but even then they say the weeds will probably still come back.
At this point my primary goal is just to stop having to cut out trees all the time. Aside from the fact that we don't have thousands of dollars to spend on this, we're also not terribly concerned about having "weeds" (i.e. native vegetation) there; we just don't want to spend so much time and effort maintaining the weeds.
So what's the cheapest, easiest way to stop or at least greatly slow the weed growth? I'm thinking of just covering the whole hill in landscaping fabric. Lowe's sells this gray woven landscape fabric (Tyvar brand, I think?), the kind that lets air and water through, with a 15-year warranty, which I could cover the whole hill with for about $100. But the issue is, the hill is too steep to cover with mulch; it would all just slide to the bottom. My question is, if I just install the landscaping fabric (pinned down) with nothing on top of it, how effective would that be?
Or what about thick black plastic sheeting instead? But I think the sun will destroy that quicker than the fabric, right?
I did spray an entire large (~2 gallon?) pump full of Round-Up onto the hill last year; it took forever and had virtually no effect on the weeds. I think they briefly turned yellow like they were dying, but came back just as strong a week or two later. And I'd rather avoid herbicides if possible.
Thanks for any suggestions.