@azi:
No, there is no requirement to stand during leining, but I know several people who have that minhag. The reasoning is that we all stand for Kriat Aseret HaDibrot, but the entire Torah is from the same holy source as the Aseret HaDibrot, therefore why should the Aseret HaDibrot receive more kavod than the rest of the Torah?
Possibly that minhag extends to the direction one faces during kriah. I should ask one of my friends who holds by it.