Could it be that the cusion is too thick? If you put a thinner pad on that seat, so that your feet were closer to the floor, would the arms be too high? I am doubtful that using weights to shift its center of gravity would help much, and the only other idea I have is to shorten the legs and make new rockers, which would take some doing.

I second that thick cushion. Does it have springs in it or just a pad?
Linda C

IT is just a foam cushion. But sitting lower in the chair does not help, as with the center of gravity lower the chair does not want to rock back at all. Would taking the rockers off and lowering the rear posts about 2 inches make it naturally lean back instead of naturally lean forward like it does now?

That's probably the direction I'd head in, though I wouldn't take off 2" all at once.

In school I watched a fellow student design and build a rocking chair. The shapes and relationships seemed quite subtle, and he did a lot of experimenting before he got it right.

I can't tell for sure what sort of joinery was used between the legs and rockers of your chair, but I'm guessing dowlels, the holes for which won't line up anymore when you start cutting parts of the leg away. That's why I think you should be prepared to make new rockers.