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The reason is the amount of html coding in the file in comparison to the amount of content. So if you have a 15k file, and 13k of it is html and only 2k is content, then it won't rank well. On the other hand, if you have a 15k file with only 2k of html and 13k of content, the search engines will really like the page.
As for the keyword question, each sub-page into your site should usually focus on a more specific topic that your site talks about.
Example - a books website.
Index page should have "Books" or something similiar in the title and first P.
First page in should focus on a certain type of the product, so the title should be something like "Science Fiction Books".
Second page in should be even more specific, perhaps narrowed to a specific manufacturer or set of products, "Science Fiction Books by Douglas Adams".
Third page in should be very specific to one very narrowed topic, "Hitchikers Guide to the Galaxy, a Book by Douglas Adams".
This is just an example and you'll have to adjust it to your specific site. But I've found it's the most effective.
As for your columns, ideally the first text in the first column would say something about your site. So if you want a link exchange as your suggesting, then I'd go with a basic section title like "Book Websites", and then list off your links below that title. A "submit your url" link or whatever you call it should probably be the last item in that last.
IMHO, there is no definitive answer to your question, since there are highly successful sites that take either approach. For example, some vertical sites carry important kw's throughout a majority of pages. But a broad news site would tend to get most of it's kw driven traffic from the topical content on each subpage...regardless of the presence of the kw 'news'.
It is also the case that subtle, and not-so-subtle, changes can occur along these lines, with the ebbs and flows of algo changes. For example, it is possible that G's recent algo changes have made it more difficult than was previously the case for subpages of vertical sites to rank well for specific variations of site-wide core phrases. Just a preliminary observation.