Single ply vs. double ply hand spun for a weaving project.

My next spinning/weaving project will be a small rug made out of the yarn I create from the undercoat of my golden retriever/shepherd mix. I intend to use a generic cotton warp. Generally I make a double ply yarn for knitting, but am wondering if a single ply might have advantages for weaving.

While the double ply would be more balanced, a single ply might have a smoother look to it when woven.

Any advice/suggestions?