Does a letter of recommendation from a postdoc who's been my instructor carry much weight?
The issue with getting a letter from a post-doc is not their job title; it's the degree of experience they have with different students, and the authority with which they can judge their preparedness for a graduate program.  So, it's not that a letter from a postdoc is unacceptable and as soon as they have an assistant professorship everything is great.  There's a subtle continuum where the more experience someone has, the more weight their letter has, because they have known so many more students.  

Also, this is a bit more cynical, but humans are social creatures.  It's well-nigh unavoidable that they give more weight to a letter from someone they know personally.  A postdoc is much less likely to be well-connected and thus able to leverage this for you.