I have never heard about one side being preferred to the other and I have shown in A shows before (although its been a looooong time).
Also, the weights is a good idea, however I would also worry about the horse ripping them out if they got caught on something.
I would prefer the sleezy over anything simply because it reduces the risk of mane getting ripped out but if you have your horse where you can monitor them (like in a stall or such), you could reduce the risk of them getting it caught somewhere.
Maybe it's a British thing? I see you're in the USA :)
Huh, I didn't think there was a preferred side. I thought it was whatever the way the mane grew. I think Gizmo's is on the left when facing him. Except for that little bit on the top that likes to fall over to the other side.
Just to add my 2 cents I've heard from several show people that apparently the mane on the right side is right and the if it falls on the left it is wrong. I'm not sure but I think they just said its something to do with showing them.