Welcome, I am Chris (aka-Moose)
Since it will occur in neutral that means it has to be the engine, transmission, or exhaust. Since weight effects it, that means its the mounts or the exhaust. My suggestion is to watch the engine and transmission when shifting back and forth between drive and reverse to see if it moves excessive indicating a mount is bad. Next raise the vehicle and check the exhaust hangers, then loosen the exhaust system, give it a good shake to relieve any mounting stress then bolt it all back together.
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