Here's the College Board's compilation of the way various colleges use the SAT scores in college admissions:

http://professionals.collegeboard.com/profdownload/sat-score-use-practices-list.pdf

It looks like there are two main themes.
1) Some colleges consider the highest scores in each subsection across all administrations of the test ("superscoring").
2) Some colleges consider the highest additive scores from a single administration of the test.

The document lists specific colleges and their policies, although I suppose that might be subject to change.
I don't see any college saying they average the scores.

I have heard an admissions director at an elite university say that, above a certain "threshold", small variations in SAT scores make very little difference - for those applicants above a certain level, other factors such as grades, recommendations, extracurriculars, essays, etc, are the deciding factors.

Another thought - I would bet that a kid who scores very highly in middle school would score about the same or better as a sophomore or junior in high school.

Hope that helps.