I know you've mentioned that you've tried the row-weights on the block page and it hasn't worked, but this is 100% definitely the correct way to order blocks within regions. For example:
In that example the Search Form comes after the main page content (which is a block in Drupal 7), which includes the node content, for every page on which it's active. I've tried it with blocks made from Views as well and it work exactly as expected.
I guess it's possible that you have some theme preprocessing/template override that might be re-ordering the blocks but I can't imagine why you'd have that and not know about it.
If that's not the case the only thing I can really suggest is check to make sure you don't have any rogue CSS causing that particular block to appear above the node content. It's a long shot but it may be the case.
If you've checked your theme's template.php file and page template files, and the CSS, and it still doesn't work, I can only advise re-installing/overwriting your Drupal core files as it's likely there's something wrong with the one you're currently working with.