First off, I like your quilt - the rows of black diamonds are different from anything I've seen before, and I think it will be really striking in the end.
I whip stitch my hexies, like you, and I understand your pain; no matter how well you sew, the stitches always show. I try to use a matching or neutral thread that will blend in. I would suggest that you use a medium-dark grey, since most of your seams include a black half. Right now I think your stitches are standing out because they're white on a fairly dark background.
Using a finer thread will help, too. I got some silk thread for hexies. I hated it at first, but now I like it. It's 100wt, so very thin. It has more of a sheen than cotton, so at first I felt it stood out way too much, but now that I've matched the tone better it isn't nearly as noticeable.
I've been looking at the Silamide thread Geri B. suggested; I think it will be my next experiment.
What size are your hexagons? If they're 1" on a side, then your stitch size is good. If they're bigger than that, you you could try smaller stitches. Also, it looks like you've taken out the paper pieces, even on the edge rows. If you're taking the paper out before you join all sides, it will be much harder to keep your stitches consistent.