I have bows cut 1/8 inch from center, to center and 3/16-inch past center. The past center should be the easiest to tune, but for me, they're the hardest. I invariably have to shoot a very stiff arrow or build out the side plate. On the other hand, I find my cut to center recurves, and cut 1/8 from center longbows shoot a wide range of wood spines well -- from bow weight at my draw to 20# more.
I don't know the geometry of it, but when the string slips off the fingers, it moves to the left for a right handed shooter. Having the arrow pointed left of the string to begin with, rather than bisecting the string, seems to somehow get the arrow bending the proper amount at the proper time and works better with a finger release.
You could be having problems with your form. Plucking will send the arrow left (appearing stiff). When your release is consistent, do you shoot both weight arrow well? All your shafts are the same diameter, right. Changes in shaft diameter will change arrow flight/impact.