Check the motor carriage rollers/glides. It may still have the original rollers. They can wear in an oblong shape since the don't make a complete 360 degree rotation when clutching. They also break or go missing after long term use. Also, check for missing or broken motor carriage springs. Overtime, the motor carriage accumulates dirt and starts to hang up and motor carriage and trans belt won't "clutch" properly. The motor carriage should glide smooth and snap back with authority when pushed towards the transmission.
Also, remove the belt from to the pump and twist the pump pulley. It should turn smooth and linear. If it doesn't, grab some Zoomspout turbine oil from your local appliance outfit, remove the flathead screw from the center of the pump, and shoot some turbine oil in there.
The pump belt is designed to run loose on these machines. If the pump hasn't been touched since it left the factory, chances are it's adjusted for proper tension.