[Unclenick]

As I said, the difference is due to the difference in barrel time. If the pressure is the same, the 700 grain bullet will only be going half as fast by the time it gets to the muzzle. That means it has spent twice as much time in the barrel being pushed forward by that same pressure. Since essentially that same pressure pushes back equally and oppositely against the gun, the gun, being the same mass it was before, will have been given twice as much rearward momentum because it was pushed back for twice as long.

The concept you actually want is called impulse. It is the application of a force multiplied by the time over which it is applied. The longer the force is applied, the more it accelerates a mass (in this case the gun mass) to a higher velocity. Mass times velocity is momentum, and that's what the gun gets more of. It will feel closer to four times more recoil because your nerve endings will sense in proportion to kinetic energy rather than momentum. That's because your shoulder is stopping twice the momentum in roughly half the time, and that takes four times the force. Recoil should feel roughly doubled when the bullet plus powder charge is about half-again heavier.

The force is just the pressure times the cross-sectional area of the bore. In a real calculation that part of recoil against the breech is actually the sum of the force against the bullet base and an average of about half the powder mass being pushed forward, too, plus you then get the rocket effect impulse added to it. Quite a bit going on there.