Bigger wire diameter may not mean anything with aftermarket coils. Besides wire diameter, the specific alloy and coil spacing also plays into spring rate.
Yeah, the overall rule is wire diameter + length. Thin wire+few turns can be equivalent to thick wire+more turns.
If you picture the spring unrolled into a rod with one end attached to a vice, it's "obvious" that you can bend the end of a long wire easier than a short one, if a given diameter. That's more or less what's going on.