[dsraven]

nice looking truck.
for starters block the front wheels, fore and aft, and then jack the rear up and place it on stands on the frame, not the axle. release the park brake and then grab each wheel and see if there is movement of the axle laterally in the axle tube (in and out from side to side). a little bit is normal because the axle is held in place, so it can't just pull out, with a "C" clip that fits into a groove on the end of the axle at the middle of the axle housing. you could google it for a better description with pictures. anyway, sometimes the groove or the C clip wears and can cause some movement. the axle butts up against a large pin in the middle of the differential and that is what keeps it from pushing in further than it should. sometimes the end of the axle can wear where it butts up against that pin, or the pin can wear in that area. if you get a lot of in and out play in the axles then it would be worthwhile to take the cover off and check to see what you have for wear inside on those parts.
if the axles have the normal amount of in and out movement then start checking the spring end bushings and pins and spring hanger mounting integrity. do the same check on the shackle pins and bushings. check the axle mount U bolts and plates as well to ensure they are tight and not allowing the axle to move on the springs. if everything is in good shape there should be little side to side movement.
are you using original style frame mounted spring hangers and pins/bushings?