Brands that make soft, 100% cotton baby clothes (sensitive skin)

My baby has pretty bad eczema, and he is currently outgrowing most of his clothes.

I'd like to get soft, lightweight, 100% cotton clothing from here on out (we live in a warm climate). Ideally zip or button ups, so nothing has to go over his head and face (I know onesies can go up the other way...but the shoulders always seem to get stretched out when I've tried that).

I have no idea what brands to look at. We need softer bibs & washcloths, too.

EDIT: baby is long and lanky, so something that runs narrower would be best

EDIT #2: Thanks for the ideas everyone!