Make sure when you drill the blank you are perfectly down the middle..It looks as you turned the blank down and it centered,becoming round it caused it to be heavy on one side of the knot...I hope this made some sense and was of some help.
As Eric said, you must drill exactly down the middle of the blank. Also, the thickness of your insert material must be exactly the width of your saw kerf. If you are out by even a very small amount, the knot will not be symmetrical.
I did match the insert material to the saw blade so I guess I was off on the drilling part. I went back down to look at the blank and I think that it is not square. It is pretty close, but with this kind of thing close doesn't cut it. I guess I need to run them through the table saw to square them up before I start any segmenting.
Thanks again for the insight. It helped me to at least look at it again to figure out what I was doing wrong.
The picture you have posted makes it a little difficult to see the problem. Could you post another picture looking directly at the point where the two rings cross and another with the barrel rotated 90° so the cross is not visible at all. Thanks.
And, yes, not having perfectly square blanks can be a big problem, too.
Randy, thanks for taking a look at this. I tried another one last night and found that the blank was just a bit out of square. Once I ran it through the table saw one side needed a trim which squared it up. I did the inlay again and this time they were perfect. The square blank and the centered drill hole fixed the problem. Thanks again everyone.