How can I manipulate MySQL fulltext search relevance to make one field more 'valuable' than another?

Well, that depends on what do you exactly mean with:

I want a row with foo in the keywords to have more relevance than a row with foo in the content.

If you mean that a row with foo in the keywords should come before any row with foo in the content, then I will do two separate queries, one for the keywords and then (possibly lazily, only if it's requested) the other one on the content.

I needed something similar and used the OP's solution, but I noticed that fulltext doesn't match partial words. So if 'watermelon' is in Keywords or Content as part of a word (like watermelonsalesmanager) it doesn't MATCH and is not included in the results because of the WHERE MATCH. So I fooled around a bit and tweaked the OP's query to this:

SELECT *, 
CASE WHEN Keywords LIKE '%watermelon%' THEN 1 ELSE 0 END AS keywordmatch, 
CASE WHEN Content LIKE '%watermelon%' THEN 1 ELSE 0 END AS contentmatch,
MATCH (Title, Keywords, Content) AGAINST ('watermelon') AS relevance 
FROM about_data  
WHERE (Keywords LIKE '%watermelon%' OR 
  Title LIKE '%watermelon%' OR 
  MATCH(Title, Keywords, Content) AGAINST ('watermelon' IN BOOLEAN MODE)) 
HAVING (keywordmatch > 0 OR contentmatch > 0 OR relevance > 0)  
ORDER BY keywordmatch DESC, contentmatch DESC, relevance DESC

Hope this helps.

As far as I know, this isn't supported with MySQL fulltext search, but you can achieve the effect by somehow repeating that word several times in the keyword field. Instead of having keywords "foo bar", have "foo bar foo bar foo bar", that way both foo and bar are equally important within the keywords column, and since they appear several times they become more relevant to mysql.

We use this on our site and it works.