I don't know if there is anything you can really do about it at this point, since you have already started quilting it, but I'm pretty sure that quilting is going to help.
Because I do machine quilting, I use a lot of starch when construction my quilt tops, but that is probably not something that you want to do for hand quilting. I'm anxious to hear how this works out for you!

Thank you Margo for your suggestions. I am quite confident that the blocks and sashing are measuring correct. I did get lazy with the border and could be off there, however, I took the borders off and still had the same problem with just the quilt top. Somehow I wonder if it has something to do with the fact that the appliqued block seem to be more stablized than the sashing. Do you think that I will help it by doing a tight hand quilting. Some years ago I did a small six-sided piece that did not lay flat when I put the binding on it. I went back and quilted close together in the outer border and it totally took care of the problem. I think this is the first on-point top that I have done. I may just chalk it up to a learning adventure, only, it would be nice to understand what caused it.

Grammerann, were all of the blocks exactly the same size before you added the sashings? Did you cut your sashing strips a uniform length and width? When you added your 4" borders, did you cut them the length that the quilt measures through the center horizontally and vertically? Are your seam allowances consistent. Were your setting triangles on the sides cut large enough?
Fullness can come from a number of issues, especially with an on-point setting.
It sounds like maybe your borders are not equal lengths, but I'm not sure where the fullness is coming from. Could you post a photo?

I just finished a twin bed sized top and am having a terrible time trying to get it to lay flat to sandwich it. The top is made up of 7 1/2 inch machine appliqued blocks. The applique covers most of the block leaving a stained glass look. The applique was affixed with "Steam-a-Seam 2" and then machine blanket stitched. I set the blocks on point with 2 1/2 inch sashing. All material is 100% cotton, quilt quality fabric from my local quilt store. I put a 4 inch border around the quilt. It just will not lay out flat. When I pin out one side the opposite corner pulls in. The applique blocks are relatively stiff, while the sashing is quite soft. I am now attempting to hand quilt the sashing with a 1/2 inch cross-hatch - my hope is that this will stabilze these pieces and bring it into shape. I have been quilting for many years, but have never used this method to applique before. Has anyone else had this experience and what remedy can you provide.