Let me go against the grain on this one... ITS OKAY to leave your crawler in there!! Not sure where these opinions are coming from.
Flat spots take months to years... (sun rotting tires out is usually more of an issue)
suspension is plenty stiff enough (that's what its built for and usually a hell of a lot stiffer than your vehicles)
Now, to back this up.... Same axles... 16' trailer... and 4500# rig... left on trailer for years...about 3 to be exact
We Would move trailer every few weeks when wheeling, sometimes not for several months.
Unless your trailer specifically states it needs to be kept unloaded (which I cant imagine any trailer would), then don't worry about it... the only thing you have to worry about is someone jacking your trailer AND your rig...