06 Freightliner Columbia: Air Issues only when loaded

I'm guessing you have the airliner suspension. I'd go to the T fitting that goes to the right side and crack that line to make sure you have air flow.
The other thing would be a bad pressure protection valve,but that should restrict air to all bags.

 

Single or dual leveling valves?

Not loading heavy on the passenger side are you?

 

did anyone replace the valve at some point the other thing is depends where yoiu are in the country but it could be leveling valve freezing up. just open up the ports of the air bag that 's not getting inflated and see if you have good air supply coming there if no chase it down to the leveling valve make sure there is no kink in the line