First, love your quilt top. I have that pattern, and bought the fabric. Yours is gorgeous.
As far as the back is concerned, it looks like it was quilted heavily in the blue hexagons, but nothing in the pieced snowflake ones. The quilting needs to be balanced thru the whole quilt. You would need to pin or baste the snowflake blocks and then quilt them, maybe just SID on all the seams. I think that it will improve the back, but probaly not remove all the fullness.
Looks like the backing was not stretched enough when the sandwich was made.