Ask Mr. Smarty Plants

One word: grasses. In the first place, that is probably what you are calling "weeds." In the second place, deer rarely touch grasses. You really answered your own question without knowing it. You might like to look at our list of Deer-Resistant Plants for help with plants besides grasses. All of the 8 grasses and grass-like plants we have selected are tolerant of acidic soils and shade to part shade conditions. We would suggest you also contact the Penn State Cooperative Extension Office for Allegheny County. They may have a list of grasses for your purpose better than ours because they are working from experience. 

We recommend grasses for controlling erosion because of their extensive fibrous root systems that serve to hold the soil in place.  However, seeding grass is not the whole process.  The seeds need moisture to germinate.  If the moisture comes in the form of rain, it is likely to wash the seeds down the bank  before they have a chance to germinate and take root. An erosion control blanket in which the erosion-control fabric works by slowing the runoff water allows sediments to fall out rather than be washed away. Seeds are sown under the erosion-control material and grow up through the matting when they germinate. You can also insert plants into the soil by cutting through the matting. The roots of the plants that are growing through the erosion-control material anchor the soil to stop the erosion. If you use erosion-control blankets made of biodegrable material, they will eventually disappear leaving the plants to control the problem.  Many nurseries carry this erosion control fabric, and can give you help in how to install it. 

We will go to our Native Plant Database and search for grasses native to your area in and around Allegheny County, PA, USDA Hardiness Zone 6a. We will stipulate in our search "part shade" (2 to 6 hours of sun a day) and "shade" (less than 2 hours of sun). Follow each link to the page on that plant in our Native Plant Database to learn its expected size, sun needs, propagation, growing conditions and soil types.

Grasses for hillside in Allegheny County PA:

Andropogon gerardii (big bluestem)

Carex blanda (eastern woodland sedge)

Calamagrostis canadensis (bluejoint)

Carex texensis (Texas sedge)

Chasmanthium latifolium (Inland sea oats)

Elymus canadensis (Canada wildrye)

Muhlenbergia glomerata (spiked muhly)

Schizachyrium scoparium (little bluestem)