"The arching of the back is to counter balance the action of the lady."
Well first, she's not really supposed to be arching her back either, but we know she will.
More importantly, the "counterbalancing" is visual, not physical. There is no need to counterbalance her weight. And because of that, all we need to achieve is the visual effect.
To an inexperienced observer, it may look like the man is arching his back (and an inexperienced man may well be doing so) but what is actually happening in a good dancer is that the vast majority of the position is created in his lower body. His upper body continues to grow out of this with a fairly straight torso - it's just that the position of the legs and hips makes the torso look much more curved than it actually is. On a good dancer... a bad one of course will break at the waist!