>So, tying the band onto your barbell will give you more
>resistance on the downswing, right? Otherwise, why not just
>add more weight?
Barbells and dumbells have the most 'tension' near the bottom of the move, while bands have the most 'tension' near the top of the move, so combining them emulates some types of weight equipment that has even tension throughout the move.
Keli Roberts showed some dumbell/band combo moves in Shape or some other magazine a while ago. I thought it was a very effective way to change up resistance and give the muscles a challenge they aren't used to. Not so sure about the bands and bar, though.