How does "time odds" confer an advantage to the weaker player? Ok, we set the clocks so that the weaker player gets 15 minutes on the clock, and the stronger player gets only five. In theory, that gives the weaker player three times as much time to think, which should be an advantage.

Except that the stronger player can use the weaker player's time to think. OK, the weaker player has "extra" time to think out a response to the stronger player's last move, but the stronger player can be thinking about the same possible responses (and more). When I am the stronger player (seldom), I can usually anticipate the weaker player's response, plan my countermove, etc., all on the other player's time. If a computer were the stronger player, this advantage might be even more pronounced, because a computer can "think" in nanoseconds.

Apparently, this is not the way things work (yours truly aside)? So how does a time advantage confer a meaningful advantage to the weaker player? Is it necessary to force the stronger (human) player to "look away" from the board during the weaker player's turn so that the stronger player doesn't benefit from the weaker player's time?
Indeed, you can think on your opponent's time. However,


Your opponent may make a move you didn't expect
Your calculation may be slightly worse because you had to see one ply farther
Even if he played a move you expected, you may have been looking at four possible moves of his, so you only spent 1/4 of your thinking time on the move he actually made
If he played his move relatively quickly, you're thinking on your own time basically from the start


As you point out, having less time doesn't give you as big a disadvantage as it might first appear. However, it is still a real disadvantage. If you think the penalty is not great enough for a given match, just increase the time difference.