The 6 is not the most 'plush' riding bike I've ever owned,,,
Hard to say exactly what's making your back hurt,,, Posture/position, 'road jolt', etc,,,
Without knowing the cause, correcting the issue could be tough,,,
I like to start w/inexpensive stuff first,,,
Air pressure in tires???? (I had a bunko gauge that read 4 lbs less than actual, so I was at 44 iso 40) Correct (for you) pressure will not make a new bike out of it, but every bit helps. {I'm currently 38 F 40 R, and I'm just north of 300 lbs.}
Make sure your gauge is accurate.
Opinions do vary, but I'd run a few less lbs of pressure than the 'popular consensus', tire wear be damned, if it meant the difference between riding or not.