You might want to consider Sedums.
Many are ground covers under 6", a lot are less than 2"
- they don't like a whole lot of watering and will drown if they sit in pools
- they flower in spring (most have yellow flowers, some pink, some cream)
- they spread but not as rapidly as other ground covers
- they can be propagated just by breaking off 'leaves' and spreading them around the soil
- they love the sun and sandy or fast draining (especially rocky) soil, a slight slope is ideal
- they don't need fertilizer or pesticides
- they tolerate some light foot traffic but not pathways
- they are evergreen or change color in the winter, a very few disappear in winter and re-emerge from seeds
- their leaf colors range from gray, really blue gray, dusty light green, vivid chartreuse, reddish green, pinkish green, yellow green, and on to all the other greens from pale to very rich dark green
- they prefer a warmer climate (like LA county or warm NC which does get some snow) but will die in places like WI and VT because of the wet of snow and soggy roots, and perhaps not enough summer
- they live forever - one of mine was found thriving in the yard of a house a hundred years old.

The first year you would have to remove the weeds but thereafter they tend to grow so close together that there isn't enough room for weeds except some fine grasses and Oxalis.

Look at Sedum kamtschaticum which makes a slight mound, quite showy flowers, reddish winter color, and will spread quite quickly the second year (from 4" pot grows to 24" wide), and Sedum acre, which I call 'take over the world' Sedum, a light green with yellow flowers that will spread very, very quickly without mounding in sun or shade and will even drape over rocks, but also will smother small annuals and perennials.

I sell a variety of Sedums at a local farmer's market and trade them on Exchange pages. Everyone gets hooked on them because they are so very low maintenance. A lot of people use them in containers and around rose bushes and shrubs as a living mulch. Many of my customers have ended up with whole landscapes of Sedums made up like tapestries since there are so many leaf and flower colors, leaf and mound shapes and differing heights. Nothing seems to bother them except chickens who eat the small ones like jelly beans and deer who only eat the foot or more tall ones. Even slugs ignore them. If it gets very cold in the winter they do shrink back some but regroup in spring with a new flush of leaves. They are quite unique in the plant world, I think.

Since you have a large area to cover you might want to consider doing a deal with a wholesaler online to buy multiple flats since a 4" pot usually costs about $4 and would be quite expensive to cover your area that way. I do not sell mine on line, I just sell locally or trade small quantities to get people addicted like me.

Nancy the nancedar

Here is a link that might be useful: Sedum Photos