I should have stated that the forces on the weight changes direction with accelleration and decelleration of the weight, not with the direction of the weight moves. I will give the somwhat lame excuse that after an entire day of problem solving at work I'm tired and make more mistakes.

If I would guess, then the 90 degree is to give the counteracting effect/force due to the decellerating weight  a larger lever to work on. The direction of the total force changes when the recoil force is gone.

With the revisions:

This is how I understand the system works (version 1.1):

- 1 Muzzle climb is reduced by the lower position of the barrel in relation to the shoulder/wrist. The lower position directs the recoil forces better into the shoulder/wrist, because the recoil has less leverage to turn the barel upward.

-2 The recoil force accellerates a weight downward, which causes the barrel to rise due to an upward force and builds up kinetic energy in the moving weight that forces down a spring. When the spring decellerates the weigh, the force reverses, wich causes the barrel to move downward. Also because most of the recoil is propably *1) gone the resulting force vector form the recoil and the weight forces changes direction (angle) and works on a different (larger) lever if one assumes the shoulder/wrist as a pivot point. The weight will propably *2) be accellerated upward until the bolt strikes/detonates the next bullet. So when the next bullet is struck the barrel is approximately in the original position. Then the weight is decellerated in the other direction by the recoil and the vector of the recoil and the weight accelleration changes and with that the lever and the whole thing starts over again.

*1) Assuming the weight decellerates when the bullet has left the barrel, which the following picture suggest.
*2) They could use non linear springs (variations in pitch on the spring windings), or use a combination of 2 springs.
      There could also be all kinds of non linear effects in the cam mechanism that forces the weight up and down.
      With the right kind of cam shape you could make the weight have a different characteristic when it moves up from
      When it moves down.

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