What is a small fat bird with a short tail and gray or brown feathers?

Well that depends how much black and brown you are talking about. Let us start with the Common Grackle. Merging from juvenile to adult it is brown with black on the wing. Then there is the Brown-headed Cowbird. It is black with a brown head. The Black-headed Grosbeak has a brown speckled breast and the rest is black speckled with white points and lines. And the Bohemian Waxwing is a light Brown with Black wingtips. There are various other small backyard birds that are brown and speckled with black.