My drone has a takeoff weight of 13kg and a fully loaded weight of 18kg. The payload is gradually dropped after takeoff, so under the same set of PID parameters, either the unloaded or fully loaded condition always performs poorly. Are there any compensatory parameters for this?
No, that feature is not available, but can be implemented in a lua script.
You should tune with minimum payload weight and then change the ACCEL params based on the TOW.
Here is another thread: Weight Changes While in Flight