Due to a back injury, Tweek is partially paralyzed in his hind quarters. He can use his hind legs only with difficulty, but will stand on them if he wants something badly enough.
He also has a wheelchair and gets around great in that. In the first video below, we see Tweek in his wheelchair befriending a stray cat whom the family had to adopt since Tweek loved the kitty so much. In the second video, without his chair, Tweek goes on a wobbly quest to find the kitty.