Acrobat can delete a layer via the layers sidebar, but ONLY if that layer is empty of content and unlocked - click to select it, press delete - if nothing happens, there's content on it.
You can add a new layer from a file, rename layers, merge two or more layers into one or flatten the document completely using the layers sidebar Options pulldown, but you can't re-shuffle their stacking order or move things between them (the simplest way to do advanced stuff like that is to import the PDF into something that respects layers, such as Illustrator, edit it and export it back again.
You can add a new layer from a file, rename layers, merge two or more layers into one or flatten the document completely using the layers sidebar Options pulldown, but you can't re-shuffle their stacking order or move things between them (the simplest way to do advanced stuff like that is to import the PDF into something that respects layers, such as Illustrator, edit it and export it back again.