multiple enchantment types

[AuraSeer]

So no increase in base cost of powers just as there is no increase in cost for doing both parts of a double weapon. Is that because a weapon is not considered " one that takes up a specific space on a character"?

For double weapons, the cost isn't increased because you aren't using both enhancements at the same time. If you have a double-ended sword with one flaming end and one shock end, it's not the same as a single flaming shock sword. You attack with the each end separately, as if you were dual-wielding separate weapons. So getting the two heads enhanced is not any more advantageous than having two separate weapons enhanced.