You've got to be kidding. I'm not even going to provide a link this time (but I'm fairly certain that some commercial posters will thoughtfully supply you with theirs once this thread is ferreted out ).
Originally Posted by tkamiya
I don't believe you are using the term "backing board" in a standard way. You mount – dry, hinge, or whatever – the art to a mount board. The flat artwork, in this case a photograph, is normally separated from frame glazing and "finished" for presentation using a window mat. Thickness of both are determined by the size of the print's necessary support, and aesthetics. Most "professional" presentations use 4-ply (8-ply for very large "mural" prints) mount board, and 8-ply window matting material. Amateurs (don't get excited, it's just an accurate term – look it up) tend to use less expensive 4-ply mat for windows. These elements form the basis of a well (standard) presented print.
That said, and to answer your specific question, backing board can be whatever you wish as long as it supports the presentation in its frame and conforms to general archival standards, that is, acid free for monochrome photographs. The thickness is only as necessary as can be accommodated by the frame's depth, minus glazing. As a consequence, there will have to be some forethought in frame selection. I have older shallow glass frames that have a tough time accommodating the print and and any backing material. For that reason, I prefer metal Nielsen frames that are at least 1 to 1.25 inch deep, and can take anything I throw into it. And these days I throw relatively inexpensive, easy to cut, super lightweight, 1/4 inch acid free paper faced "archival" foam core. It is robust enough to support and protect all sizes of my prints within the frame. I have even hinge mounted some color prints to it.
I have seen 2-ply and even 1-ply mat board used to dry mount prints, sometimes flush cut. These are then mounted loosely to 4-ply as you have suggested, or with photo corners. The general strategy here seems to be a way of subverting museum considerations of not permanently affixing "the print" to its mount (congratulations if that's relevant to you). So this now becomes a possible confusion of what then is actually considered to be backing board. I would advise using additional support, as previously indicated, when framed.
I believe that's a lot more information then you deserve from an "amateur" who doesn't troll the site everyday with unsolicited, unsubstantiated, opinion or non–commercial agenda, given your somewhat snotty remark.