I started playing the game again recently after a long break. Now before the removal of soft caps I felt that weapon enchants were still weak but not pitiful as they are now, as other damage has gone through the roof. Basically, other than the potency and quality of the runes, the magnitude of weapon enchants do not scale with anything. The only thing that I know of is the 5th bonus of Torug's Pact, which increases the potency by 30% and reduces internal cool down by 1 second. Honestly i'm not a big fan of the cool downs of weapon enchants; not only does it really weaken the enchants themselves but also it seems silly, and its completely different than how it worked in TES single player games. Besides, don't all weapon types have the same attack speed anyways? If not, just adjust the magnitude to the speed of the weapons, simple.
Even with Torug's Pact, and dual wielding 2 purple weapons with the powered traits, with a purple flame enchant on each, if I were to spam light attacks on an npc, I would do about on average 300-500 dps depending if I've gotten the burning proc. This is at V10; the damage is quite pitiful. The damage gets even worse when you start using abilities and heavy attacks. The only real uses of such enchantments is simple flavor, and the occasional explosion proc that you can get if the npc is weak to that element.
I think the best way to address this weakness is to somehow find an appropriate way for the potency of these weapon enchants to scale with certain stats, maybe reduce the base cd as well. Since weapon and spell damage can be scaled and is basically without a limit, this leaves enchant damage to dust. The first thing I can think of is to add multiple ranks of a passive within enchanting that increases the potency of enchants other than what qualities you can create. Alchemy has a passive within that increases duration of potions so I think it would be fair. Increasing the base enchant magnitude would help as well.