Conflict Resolution Mechanics

First, I suggest having 6 health instead of 3.
3 will be going a bit to fast for the next mechanic. But technically speaking, each creature will have the damage/health ratio on 3.

With only 2 types, you can have a RPS system. It reminds me of only Infantry and Tanks.

Light weapons defeat Dark creatures.
Dark weapons defeat Light creatures.
This effect by a factor of ..., but even that can vary. I suggest to keep an average with whole numbers. Back to that later.

Now, Light creatures can carry either a Light weapon or a Dark weapon.
And Dark creatures can carry either a Light weapon or a Dark weapon.

There for you have 4 different types.

You could say, a Light weapon does 1 damage against Light creatures. But does 3 damage against Dark creatures. That is an average of 2 damage. Although it needs to shoot 6 times on a Light creature, only 2 times is needed on a Dark creature. The cost of this weapon is 1 Light.

Weapon suggestions:
a cost of 1 Light;
1-3
a cost of 2 Light;
1-7
2 x 1-3
a cost of 3 Light;
1-11
2 x 1-5
3 x 1-3
4 x 1-2
a cost of 1 Dark;
3-1
etc.

Light Creature suggestions:
a cost of 1 Light;
6 Health
a cost of 2 Light;
12 Health
etc.

You could have additional "magic" like damage reduction by 1. Thus all the 1 become 0 and are rendered ineffective. The multiple weapons are very weak to this.
Damage increaser is very strong in return to multiple weapons.

Well, I have given an idea. But I am not sure about the multiple weapons. Are you planning on expanding the game? If so, you need something better then what I just posted.

What if you had dice that determined your ability to hit, but you have the chance to affect your ability to hit by various factors.

For example, a creature has "armor" 5, meaning that an attack roll of 5 would be required to hit it. A creature that rolls 4-sided dice, even if they get a lot of dice (rolling each as independent attacks), has no chance of hitting it.

However, if a D4-creature gets some sort of bonus they can roll a 6-sided dice. A double-bonus (this allows stacking) lets them roll an 8-sided dice! Set a cap at 10s or so, and make sure that most armor is hittable, and it could totally work. In fact, I have a spreadsheet that calculates this all for you, depending on an attacker's roll and the armors you set, and even taking into account the probability of getting hit if you have more than one attack directed at you. Let me know if you want to check it out.

Granted, this means that luck still plays a factor, but it means that you get to mess with the probabilities of hitting, and you'll play strategically to get bonuses, because it's the key to landing hits with even the tiniest of creatures.

How do you get bonuses? You could allow for two attacking creatures to get a bonus for attacking together (perhaps specific to the creature). Consider flanking. Consider attacking at range, and if the target is our of range, rolling a lower dice as a penalty. Creature has a "weakness spell" on it? lower the dice (I call it "D-down"-ing).

I played with this for my large-scale strategy game a while back, but it didn't quite work out with what I was doing, so I changed it. I like to play with the idea now and again though, because I think it's a good one.

In my case, however, i was making a game similar to Risk with special ships that hit harder or confer other bonuses. I changed my idea to make any "capital ship" roll d8s while regular ones rolled d6s, and set the "hit" bar at 5. casualties were taken from the opponent's army according to their choice, but if you rolled a natural 8 on an 8-sided dice from one of your ships, you got to choose what died, and that was pretty cool.

Hope I helped...

Rune Age does combat by playing cards from hand. Star Wars does combat (edge battle) by blind playing cards from hand - which means if you play your trump and the opponent plays a chump, you've effectively wasted it. So it makes combat interesting - do you all-in or do you not?

Doomtown makes players play a hand of poker with their cards, which also has poker symbols in addition to their normal abilities, which is damn cool. So cards from the rest of the deck could be a resource for conflict too.

Otherwise I don't like dice either, and it seems like alternatives like attack/life with life tracking (tokens) is a decent way to go, if a bit fidgety. I've recently tried something like that and... so many tokens.