So, while I still am trying to work out an optimal thickness for a pro environment knife (a good balance between weight and geometry thickness), I took a recommendation from one of the pro guys here who used my knives, and ground one slightly thicker what I normally grind.
After some cutting at home, I liked the performance. It had a solid feel and I didn't see much decrease of cutting performance over thinner knives. It would make a good line knife - no flex, solid feel and thin above the edge (right now it's under .005").
Then I ground another knife even thicker at the spine but thin at the edge, and put it through the same cutting routine - apples, carrots, potatoes and onions. I didn't cut any proteins, as the purpose of the test was for an all-around knife.
The performance difference between the two was quite noticeable. On a thicker knife, the heel and middle of the knife wedged where on a thinner it didn't.
Both knives were ground to the same thinness at the edge, and approximately same convex 2/3 up the blade. The difference in weight was pretty negligible (officially 8g, but the heavier knife has a shorter machi, which probably took off another 8g from overall weight).
So, it seems to point to one conclusion - spine thickness does matter, regardless how thin a knife above the edge is. Spine thickness affects geometry in mid-section, which in turn affects cutting ability of a knife to go through denser foods like apples.
Here as some shots of spine, heel, profile and measurements. The spine shot is a bit distorted - those are not as thick as they look, but you can see a contrast in thickness well. Also, I come to think that spine measurements on a thinner knife are similar to 260mm Mario's Carter.