Quote Originally Posted by Trek420
2) Weight on the outside pedal. This means, the
outside pedal should be down (at six o'clock), and the
inside pedal up (at twelve o'clock). You should
really stand on the outside pedal, so your butt is not
on the seat, and you have no weight on the inside
pedal. Stand on that outside pedal all the way
through the turn.

This does two things.
a) it's a balance thang (insert drawl here), like carving a turn on skis
b) more important it's a safety thang. if your inside pedal is down you risk catching it on the pavement and then down you go.
c) I sometimes pedal through the turn, still keep the action light on the inside edge.
Weight on that outside pedal lowers your center of gravity which increases your stability. A tiny bit of pressure on the inside handlebar combined with this will help force your tires to grip better. Practice this last bit with a feather touch. I found I could corner tighter and faster with much more confidence.