How much does the landing gear compress on a fully loaded airliner on the ground?
The value will obviously vary for different aircraft models (and also with the loading, c.g. location etc), but the usual range can be found in the airport planning document for the particular airliner, where the values for ground clearance for the aircraft at the OEW (max. value) and MTW (min. value) would be given. The difference should give you the compression.

For example, for Boeing 737-800, the quoted value is around 15 cm (plus or minus 7cm).



Image from 737 Airplane characteristics for Airport Planning document 

Note that the different parts of the aircraft 'sink' different amounts- the fuselage sinks around 15cm, while the engines (mounted on the wings) sink more- by 16cm due to the fuel in the wings.

Another 'typical' aircraft, the A320neo sinks by about 10cm.



Image from A320 Aircraft characteristics for Airport Planning document

Note that the values are given here for max. ramp weight.