You could cut pieces of paper (with paper scissors) and sew the seams using them. This way the edges will not stretch if you pin them. I would work in quarters. Sew 4 or 5 together, lay aside, and sew each set like this. Then sew the sections together.
Another thing you could check is the circle size itself. Pin it to the ironing board and then measure from side to side, and top to bottom. Maybe that will show you if something is wrong. You could also fold it in half and see if there is something wrong this way. Hope this helps.