Typically one only jacks up one side or wheel. So of the 6000 lbs, part of the weight is supported by the wheels on the opposite side and the tow vehicle hitch or tongue jack.
Out trailer has a GVRW of about 7500 lbs. For that I use a 4 ton bottle jack along with the necessary wood blocks to get it in correct position, fully retracted, to prevent the base of the jack from being pushed into the ground.
Since our TT is a dual axle trailer, I position the jack on the frame between the two wheels in order to lift one side. Be sure to CHOCK, fore and aft, the wheels on the opposite side. Loosen the lug nuts, (you do have a proper lug nut tool don't you?) before completely jacking up the wheels for clearance to remove the flat tire and install the spare.
Bob