I'm trying to order my blocks on the top page. The behavior I'm noticing is that XOOPS processes Center-Center blocks before it processes center-left and center-right blocks.

Can this be changed? I have some left-cneter and right-center blocks that I want to display about some center-center blocks. No matter what Weight I set to the center-left and center-right blocks they always show up at the bottom of the page.

Can I modify this behavior?

Yes, it can be modified. Try to do a search on editing the theme.html file.