The armor ranking on Steel for the shield is 5 yet for the Drafwen armor (which is 10x more expensive) is 4. Which is better? Does the weight of the weapon also factor into it the damage?

Dwarven provides more protection. For comparison purposes, let us assume a character that is a master of heavy armor and all of his gear is repaired to 100%. A steel shield will provide 13.5 armor rating. A dwarven shield will provide 15. These values are good for comparison. If the character's skill in heavy armor is less than 100 or if the shields are repaired to less than (or more than) 100%, then these values will of course vary.
Reference: http://www.uesp.net/wiki/Oblivion:Armor

A weapon's weight stat does not affect its damage, although heavier weapons are often associated with weapons that do indeed deliver more damage as a general rule.
Reference: http://www.uesp.net/wiki/Oblivion:Weapons

I note that you're comparing a Steel shield to a Dwarven cuirass. In any of the sets, the defense/price ratio is highest for the shield, so if you don't use a two-handed weapon, it's the first piece of armor you should get or upgrade. However, base defense is not the only factor. The shield is the item that takes the most punishment in combat, so it will degrade fastest, and the amount of health before it's useless becomes important. After a battle, your Dwarven cuirass may still have 3 points of defense left while the Steel shield is totally broken.