Right, I hadn't considered that the back wall would actually be resting on top of the hearth pad on the floor. So, much of the weight would be addressed by gravity and the floor, with very little being supported by the wall. Thank you!You could put a sheet of plywood behind the cement board to build it out. Don't worry about the weight. It is supported by the floor and sheer strength of screws is high. The plywood spanning the studs will strengthen the wall a bit.
I'd need two layers of plywood, though, especially if the back piece is secured directly on top of the old paneling, versus on top of the tongue and groove pine we haven't installed yet.
Would it be best to put this piece on the thinner paneling, or would you put the tongue and groove boards on the entire wall first and then attach the hearth wall?