links to specs between what is normally placed on, and the size bigger that you have?
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with this being new as well. there is a good chance "air" is still within the hyd lines and cylinders. and you have not been keeping an eye on the hyd tank. to make sure it is kept full. other words dealer just installed. backhoe. filled up some hyd oil but never operated the backhoe and the stabilizers to work out the air. and if they did, they did not keep an eye on the hyd tank to keep it full as the air was purged.
are relief valves kicking in? or engine bogging down at lower idle? when you try to put stabilizers down.
double check that you have hyd hoses going to correct levers / hyd valves on backhoe/stabilizers as well.
i generally do not lift tires off ground. but will slightly take pressure off of tires. and/or raise one side to help level the rear end of the tractor. but the stabilizers should be able to lift rear end of tractor. not sure why anyone would build a backhoe were a stabilizer could not lift rear end of tractor. they are a important part of use of a backhoe.