Is it possible to access an object's Enchanting property with a script through its Ref and modify its value?

I don't think it is, although you can add multiple effects to an enchantment and have different ones active depending on certain conditions.

You could, I think, attach a http://www.creationkit.com/Papyrus_Introduction#Writing_Custom_Functions script to your object, and have its enchantment change depending on the state of a property declared in that script. Properties can be accessed externally, so if need be you could have another script modify the state of each weapon independently in order to modify its enchantment.

Cipscis

I think Wuthraad did that. You could look at its script to see how it was done.

I think Cipscis is correct. There is no way to dynamically alter Magic Effects, Spells and Enchantments with Scripts.
E.g. Enchantment.Set3rdMagicEffectMagnitude 25
Best way is to use conditionals like Cipscis suggests.
I've not yet looked at how complex those can be.
But it looks like you can set a variable in a Quest script and get the different Effects attached to the Enchantment to work off that.

That's a pity. I wanted to make a mod to transfer enchantments from one item to another. Particularly armors, so the one you decide to wear is purely for cosmetic reasons and/or type instead of its enchantments.

But thanks for the replies!

OBSE in Oblivion added this functionality.
I can assume that SKSE will as well.
They're good guys, those OBSE/SKSE team.