Check the function of the shocks by removing one end. I bound up shock will cause your issue. (My bet as to what is causing your problem.)
Check the condition of your spring shackle pins and spring eye bolts to make sure that they are articulating properly. Too sloppy or too tight will interfere with how the springs react.
Have someone stand on the bumper and jump up and down (without their feet leaving the bumper) while you look at the motion of the shackles. The action should be the same and the shackles should return to the same position (angle) comparing from one side to the other.
Measure the distance between the top of the axle and the frame on each side to see if they are the same. You may have a tired or broken spring on one side.
Carl

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission